Daily Papers

This paper reveals the phenomenon of parameter heterogeneity in large language models (LLMs). We find that a small subset of ``cherry'' parameters exhibit a disproportionately large influence on model performance, while the vast majority of parameters have minimal impact. This heterogeneity is found to be prevalent across different model families, scales, and types. Motivated by this observation, we propose CherryQ, a novel quantization method that unifies the optimization of mixed-precision parameters. CherryQ identifies and preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate the effectiveness of CherryQ. CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance. Notably, our 3-bit quantized Vicuna-1.5 exhibits competitive performance compared to their 16-bit counterparts. These findings highlight the potential of CherryQ for enabling efficient deployment of LLMs by taking advantage of parameter heterogeneity.

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models also increases. We introduce a technique to train deep neural networks using half precision floating point numbers. In our technique, weights, activations and gradients are stored in IEEE half-precision format. Half-precision floating numbers have limited numerical range compared to single-precision numbers. We propose two techniques to handle this loss of information. Firstly, we recommend maintaining a single-precision copy of the weights that accumulates the gradients after each optimizer step. This single-precision copy is rounded to half-precision format during training. Secondly, we propose scaling the loss appropriately to handle the loss of information with half-precision gradients. We demonstrate that this approach works for a wide variety of models including convolution neural networks, recurrent neural networks and generative adversarial networks. This technique works for large scale models with more than 100 million parameters trained on large datasets. Using this approach, we can reduce the memory consumption of deep learning models by nearly 2x. In future processors, we can also expect a significant computation speedup using half-precision hardware units.

The state-of-the-art (SOTA) for mixed precision training is dominated by variants of low precision floating point operations, and in particular, FP16 accumulating into FP32 Micikevicius et al. (2017). On the other hand, while a lot of research has also happened in the domain of low and mixed-precision Integer training, these works either present results for non-SOTA networks (for instance only AlexNet for ImageNet-1K), or relatively small datasets (like CIFAR-10). In this work, we train state-of-the-art visual understanding neural networks on the ImageNet-1K dataset, with Integer operations on General Purpose (GP) hardware. In particular, we focus on Integer Fused-Multiply-and-Accumulate (FMA) operations which take two pairs of INT16 operands and accumulate results into an INT32 output.We propose a shared exponent representation of tensors and develop a Dynamic Fixed Point (DFP) scheme suitable for common neural network operations. The nuances of developing an efficient integer convolution kernel is examined, including methods to handle overflow of the INT32 accumulator. We implement CNN training for ResNet-50, GoogLeNet-v1, VGG-16 and AlexNet; and these networks achieve or exceed SOTA accuracy within the same number of iterations as their FP32 counterparts without any change in hyper-parameters and with a 1.8X improvement in end-to-end training throughput. To the best of our knowledge these results represent the first INT16 training results on GP hardware for ImageNet-1K dataset using SOTA CNNs and achieve highest reported accuracy using half-precision

While vision transformers (ViTs) have shown great potential in computer vision tasks, their intense computation and memory requirements pose challenges for practical applications. Existing post-training quantization methods leverage value redistribution or specialized quantizers to address the non-normal distribution in ViTs. However, without considering the asymmetry in activations and relying on hand-crafted settings, these methods often struggle to maintain performance under low-bit quantization. To overcome these challenges, we introduce SmoothQuant with bias term (SQ-b) to alleviate the asymmetry issue and reduce the clamping loss. We also introduce optimal scaling factor ratio search (OPT-m) to determine quantization parameters by a data-dependent mechanism automatically. To further enhance the compressibility, we incorporate the above-mentioned techniques and propose a mixed-precision post-training quantization framework for vision transformers (MPTQ-ViT). We develop greedy mixed-precision quantization (Greedy MP) to allocate layer-wise bit-width considering both model performance and compressibility. Our experiments on ViT, DeiT, and Swin demonstrate significant accuracy improvements compared with SOTA on the ImageNet dataset. Specifically, our proposed methods achieve accuracy improvements ranging from 0.90% to 23.35% on 4-bit ViTs with single-precision and from 3.82% to 78.14% on 5-bit fully quantized ViTs with mixed-precision.

This is the 1st part of the dissertation for my master degree and compares the power consumption using the default floating point (32bit) and Nvidia mixed precision (16bit and 32bit) while training a classification ML model. A custom PC with specific hardware was built to perform the experiments, and different ML hyper-parameters, such as batch size, neurons, and epochs, were chosen to build Deep Neural Networks (DNN). Additionally, various software was used during the experiments to collect the power consumption data in Watts from the Graphics Processing Unit (GPU), Central Processing Unit (CPU), Random Access Memory (RAM) and manually from a wattmeter connected to the wall. A benchmarking test with default hyper parameter values for the DNN was used as a reference, while the experiments used a combination of different settings. The results were recorded in Excel, and descriptive statistics were chosen to calculate the mean between the groups and compare them using graphs and tables. The outcome was positive when using mixed precision combined with specific hyper-parameters. Compared to the benchmarking, the optimisation for the classification reduced the power consumption between 7 and 11 Watts. Similarly, the carbon footprint is reduced because the calculation uses the same power consumption data. Still, a consideration is required when configuring hyper-parameters because it can negatively affect hardware performance. However, this research required inferential statistics, specifically ANOVA and T-test, to compare the relationship between the means. Furthermore, tests indicated no statistical significance of the relationship between the benchmarking and experiments. However, a more extensive implementation with a cluster of GPUs can increase the sample size significantly, as it is an essential factor and can change the outcome of the statistical analysis.

Large language models (LLMs) achieve remarkable performance in natural language understanding but require substantial computation and memory resources. Post-training quantization (PTQ) is a powerful compression technique extensively investigated in LLMs. However, existing PTQ methods are still not ideal in terms of accuracy and efficiency, especially with below 4 bit-widths. Standard PTQ methods using group-wise quantization suffer difficulties in quantizing LLMs accurately to such low-bit, but advanced methods remaining high-precision weights element-wisely are hard to realize their theoretical hardware efficiency. This paper presents a Salience-Driven Mixed-Precision Quantization scheme for LLMs, namely SliM-LLM. The scheme exploits the salience distribution of weights to determine optimal bit-width and quantizers for accurate LLM quantization, while aligning bit-width partition to groups for compact memory usage and fast integer inference. Specifically, the proposed SliM-LLM mainly relies on two novel techniques: (1) Salience-Determined Bit Allocation utilizes the clustering characteristics of salience distribution to allocate the bit-widths of each group, increasing the accuracy of quantized LLMs and maintaining the inference efficiency; (2) Salience-Weighted Quantizer Calibration optimizes the parameters of the quantizer by considering the element-wise salience within the group, balancing the maintenance of salient information and minimization of errors. Comprehensive experiments show that SliM-LLM significantly improves the accuracy of LLMs at ultra-low bits, e.g., 2-bit LLaMA-7B achieves a 5.5-times memory-saving than original model on NVIDIA A800 GPUs, and 48% decrease of perplexity compared to the state-of-the-art gradient-free PTQ method. Moreover, SliM-LLM+, which is integrated from the extension of SliM-LLM with gradient-based quantizers, further reduces perplexity by 35.1%.

Post-training quantization (PTQ) and quantization-aware training (QAT) methods are gaining popularity in mitigating the high memory and computational costs associated with Large Language Models (LLMs). In resource-constrained scenarios, PTQ, with its reduced training overhead, is often preferred over QAT, despite the latter's potential for higher accuracy. Meanwhile, parameter-efficient fine-tuning (PEFT) methods like low-rank adaptation (LoRA) have been introduced, and recent efforts have explored quantization-aware PEFT techniques. However, these approaches may lack generality due to their reliance on the pre-quantized model's configuration. Their effectiveness may be compromised by non-linearly quantized or mixed-precision weights, and the retraining of specific quantization parameters might impede optimal performance. To address these challenges, we propose L4Q, an algorithm for parameter-efficient quantization-aware training. L4Q leverages LoRA-wise learned quantization step size for LLMs, aiming to enhance generality. The simultaneous quantization-and-fine-tuning process of L4Q is applicable to high-precision models, yielding linearly quantized weights with superior accuracy. Our experiments, conducted on the LLaMA and LLaMA2 model families using an instructional dataset, showcase L4Q's capabilities in language comprehension and few-shot in-context learning, achieving sub-4-bit precision while maintaining comparable training times to applying PEFT on a quantized model.

Post-training quantization of Large Language Models (LLMs) has proven effective in reducing the computational requirements for running inference on these models. In this study, we focus on a straightforward question: When aiming for a specific accuracy or perplexity target for low-precision quantization, how many high-precision numbers or calculations are required to preserve as we scale LLMs to larger sizes? We first introduce a critical metric named the quantization ratio, which compares the number of parameters quantized to low-precision arithmetic against the total parameter count. Through extensive and carefully controlled experiments across different model families, arithmetic types, and quantization granularities (e.g. layer-wise, matmul-wise), we identify two central phenomenons. 1) The larger the models, the better they can preserve performance with an increased quantization ratio, as measured by perplexity in pre-training tasks or accuracy in downstream tasks. 2) The finer the granularity of mixed-precision quantization (e.g., matmul-wise), the more the model can increase the quantization ratio. We believe these observed phenomena offer valuable insights for future AI hardware design and the development of advanced Efficient AI algorithms.

The recent rise of large language models (LLMs) has resulted in increased efforts towards running LLMs at reduced precision. Running LLMs at lower precision supports resource constraints and furthers their democratization, enabling users to run billion-parameter LLMs on their personal devices. To supplement this ongoing effort, we propose INT-FP-QSim: an open-source simulator that enables flexible evaluation of LLMs and vision transformers at various numerical precisions and formats. INT-FP-QSim leverages existing open-source repositories such as TensorRT, QPytorch and AIMET for a combined simulator that supports various floating point and integer formats. With the help of our simulator, we survey the impact of different numerical formats on the performance of LLMs and vision transformers at 4-bit weights and 4-bit or 8-bit activations. We also compare recently proposed methods like Adaptive Block Floating Point, SmoothQuant, GPTQ and RPTQ on the model performances. We hope INT-FP-QSim will enable researchers to flexibly simulate models at various precisions to support further research in quantization of LLMs and vision transformers.

Efficiently serving neural network models with low latency is becoming more challenging due to increasing model complexity and parameter count. Model quantization offers a solution which simultaneously reduces memory footprint and compute requirements. However, aggressive quantization may lead to an unacceptable loss in model accuracy owing to differences in sensitivity to numerical imperfection across different layers in the model. To address this challenge, we propose a mixed-precision post training quantization (PTQ) approach that assigns different numerical precisions to tensors in a network based on their specific needs, for a reduced memory footprint and improved latency while preserving model accuracy. Previous works rely on layer-wise Hessian information to determine numerical precision, but as we demonstrate, Hessian estimation is typically insufficient in determining an effective ordering of layer sensitivities. We address this by augmenting the estimated Hessian with additional information to capture inter-layer dependencies. We demonstrate that this consistently improves PTQ performance along the accuracy-latency Pareto frontier across multiple models. Our method combines second-order information and inter-layer dependencies to guide a bisection search, finding quantization configurations within a user-configurable model accuracy degradation range. We evaluate the effectiveness of our method on the ResNet50, MobileNetV2, and BERT models. Our experiments demonstrate latency reductions compared to a 16-bit baseline of 25.48%, 21.69%, and 33.28% respectively, while maintaining model accuracy to within 99.99% of the baseline model.

Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model solely based on the attention mechanism that is able to relate any two positions of the input sequence, hence modelling arbitrary long dependencies. The Transformer has improved the state-of-the-art across numerous sequence modelling tasks. However, its effectiveness comes at the expense of a quadratic computational and memory complexity with respect to the sequence length, hindering its adoption. Fortunately, the deep learning community has always been interested in improving the models' efficiency, leading to a plethora of solutions such as parameter sharing, pruning, mixed-precision, and knowledge distillation. Recently, researchers have directly addressed the Transformer's limitation by designing lower-complexity alternatives such as the Longformer, Reformer, Linformer, and Performer. However, due to the wide range of solutions, it has become challenging for researchers and practitioners to determine which methods to apply in practice in order to meet the desired trade-off between capacity, computation, and memory. This survey addresses this issue by investigating popular approaches to make Transformers faster and lighter and by providing a comprehensive explanation of the methods' strengths, limitations, and underlying assumptions.

Mamba state-space models (SSMs) were recently shown to outperform state-of-the-art (SOTA) Transformer large language models (LLMs) across various tasks. Despite subsequent widespread adaptation, little work has focused on Mamba LLMs' amenability for fine-tuning frameworks ubiquitously used for Transformer-based LLMs, e.g., mixed-precision fine-tuning (MPFT) and parameter-efficient fine-tuning (PEFT). For the former, it currently remains an open question whether Mamba's recurrent dynamics are robust to small input changes, such as those encountered during MPFT. Using dynamical systems theory (in particular, Lyapunov exponents), we answer this question in the affirmative. We empirically validate this result through several experiments, showing that Mamba SSMs are significantly more stable to changes introduced by mixed-precision than comparable Transformers, even when both MPFT and PEFT are combined. For PEFT, we show how targeting specific memory buffers in Mamba's customized CUDA kernels for low-rank adaptation regularizes SSM parameters, thus providing both parameter efficient learning and computational savings. Finally, with both MPFT and PEFT enabled, we explore the impact of instruction tuning Mamba SSMs for in-context learning (ICL) on natural language tasks. While pretrained Mamba and Mamba-2 models only achieve 38% and 82% (respectively) of the ICL improvements of comparable Transformer-based LLMs, we show that instruction tuning allows Mamba models to narrow this gap to 81% and Mamba-2 models to skyrocket over this gap to 132%.

In this paper, we explore FP8 low-bit data formats for efficient training of large language models (LLMs). Our key insight is that most variables, such as gradients and optimizer states, in LLM training can employ low-precision data formats without compromising model accuracy and requiring no changes to hyper-parameters. Specifically, we propose a new FP8 automatic mixed-precision framework for training LLMs. This framework offers three levels of FP8 utilization to streamline mixed-precision and distributed parallel training for LLMs. It gradually incorporates 8-bit gradients, optimizer states, and distributed learning in an incremental manner. Experiment results show that, during the training of GPT-175B model on H100 GPU platform, our FP8 mixed-precision training framework not only achieved a remarkable 42% reduction in real memory usage but also ran 64% faster than the widely adopted BF16 framework (i.e., Megatron-LM), surpassing the speed of Nvidia Transformer Engine by 17%. This largely reduces the training costs for large foundation models. Furthermore, our FP8 mixed-precision training methodology is generic. It can be seamlessly applied to other tasks such as LLM instruction tuning and reinforcement learning with human feedback, offering savings in fine-tuning expenses. Our FP8 low-precision training framework is open-sourced at {https://github.com/Azure/MS-AMP}{aka.ms/MS.AMP}.

Quantization has become a mainstream compression technique for reducing model size, computational requirements, and energy consumption for modern deep neural networks (DNNs). With the improved numerical support in recent hardware, including multiple variants of integer and floating point, mixed-precision quantization has become necessary to achieve high-quality results with low model cost. Prior mixed-precision quantization methods have performed a post-training quantization search, which compromises on accuracy, or a differentiable quantization search, which leads to high memory usage from branching. Therefore, we propose the first one-shot mixed-precision quantization search that eliminates the need for retraining in both integer and low-precision floating point models. We evaluate our floating-point and integer quantization search (FLIQS) on multiple convolutional networks and vision transformer models to discover Pareto-optimal models. Our approach discovers models that improve upon uniform precision, manual mixed-precision, and recent integer quantization search methods. With the proposed integer quantization search, we increase the accuracy of ResNet-18 on ImageNet by 1.31% points and ResNet-50 by 0.90% points with equivalent model cost over previous methods. Additionally, for the first time, we explore a novel mixed-precision floating-point search and improve MobileNetV2 by up to 0.98% points compared to prior state-of-the-art FP8 models. Finally, we extend FLIQS to simultaneously search a joint quantization and neural architecture space and improve the ImageNet accuracy by 2.69% points with similar model cost on a MobileNetV2 search space.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data.

Mixed-precision quantization has been widely applied on deep neural networks (DNNs) as it leads to significantly better efficiency-accuracy tradeoffs compared to uniform quantization. Meanwhile, determining the exact precision of each layer remains challenging. Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. In this work, we propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability. CSQ stabilizes the bit-level mixed-precision training process with a bi-level gradual continuous sparsification on both the bit values of the quantized weights and the bit selection in determining the quantization precision of each layer. The continuous sparsification scheme enables fully-differentiable training without gradient approximation while achieving an exact quantized model in the end.A budget-aware regularization of total model size enables the dynamic growth and pruning of each layer's precision towards a mixed-precision quantization scheme of the desired size. Extensive experiments show CSQ achieves better efficiency-accuracy tradeoff than previous methods on multiple models and datasets.

Mixed-Precision Quantization~(MQ) can achieve a competitive accuracy-complexity trade-off for models. Conventional training-based search methods require time-consuming candidate training to search optimized per-layer bit-width configurations in MQ. Recently, some training-free approaches have presented various MQ proxies and significantly improve search efficiency. However, the correlation between these proxies and quantization accuracy is poorly understood. To address the gap, we first build the MQ-Bench-101, which involves different bit configurations and quantization results. Then, we observe that the existing training-free proxies perform weak correlations on the MQ-Bench-101. To efficiently seek superior proxies, we develop an automatic search of proxies framework for MQ via evolving algorithms. In particular, we devise an elaborate search space involving the existing proxies and perform an evolution search to discover the best correlated MQ proxy. We proposed a diversity-prompting selection strategy and compatibility screening protocol to avoid premature convergence and improve search efficiency. In this way, our Evolving proxies for Mixed-precision Quantization~(EMQ) framework allows the auto-generation of proxies without heavy tuning and expert knowledge. Extensive experiments on ImageNet with various ResNet and MobileNet families demonstrate that our EMQ obtains superior performance than state-of-the-art mixed-precision methods at a significantly reduced cost. The code will be released.

Model size and inference speed/power have become a major challenge in the deployment of Neural Networks for many applications. A promising approach to address these problems is quantization. However, uniformly quantizing a model to ultra low precision leads to significant accuracy degradation. A novel solution for this is to use mixed-precision quantization, as some parts of the network may allow lower precision as compared to other layers. However, there is no systematic way to determine the precision of different layers. A brute force approach is not feasible for deep networks, as the search space for mixed-precision is exponential in the number of layers. Another challenge is a similar factorial complexity for determining block-wise fine-tuning order when quantizing the model to a target precision. Here, we introduce Hessian AWare Quantization (HAWQ), a novel second-order quantization method to address these problems. HAWQ allows for the automatic selection of the relative quantization precision of each layer, based on the layer's Hessian spectrum. Moreover, HAWQ provides a deterministic fine-tuning order for quantizing layers, based on second-order information. We show the results of our method on Cifar-10 using ResNet20, and on ImageNet using Inception-V3, ResNet50 and SqueezeNext models. Comparing HAWQ with state-of-the-art shows that we can achieve similar/better accuracy with 8times activation compression ratio on ResNet20, as compared to DNAS~wu2018mixed, and up to 1% higher accuracy with up to 14% smaller models on ResNet50 and Inception-V3, compared to recently proposed methods of RVQuant~park2018value and HAQ~wang2018haq. Furthermore, we show that we can quantize SqueezeNext to just 1MB model size while achieving above 68% top1 accuracy on ImageNet.

Quantization emerges as one of the most promising approaches for deploying advanced deep models on resource-constrained hardware. Mixed-precision quantization leverages multiple bit-width architectures to unleash the accuracy and efficiency potential of quantized models. However, existing mixed-precision quantization suffers exhaustive search space that causes immense computational overhead. The quantization process thus relies on separate high-performance devices rather than locally, which also leads to a significant gap between the considered hardware metrics and the real deployment.In this paper, we propose an On-chip Hardware-aware Quantization (OHQ) framework that performs hardware-aware mixed-precision quantization without accessing online devices. First, we construct the On-chip Quantization Awareness (OQA) pipeline, enabling perceive the actual efficiency metrics of the quantization operator on the hardware.Second, we propose Mask-guided Quantization Estimation (MQE) technique to efficiently estimate the accuracy metrics of operators under the constraints of on-chip-level computing power.By synthesizing network and hardware insights through linear programming, we obtain optimized bit-width configurations. Notably, the quantization process occurs on-chip entirely without any additional computing devices and data access. We demonstrate accelerated inference after quantization for various architectures and compression ratios, achieving 70% and 73% accuracy for ResNet-18 and MobileNetV3, respectively. OHQ improves latency by 15~30% compared to INT8 on deployment.

Quantization has become a crucial step for the efficient deployment of deep neural networks, where floating point operations are converted to simpler fixed point operations. In its most naive form, it simply consists in a combination of scaling and rounding transformations, leading to either a limited compression rate or a significant accuracy drop. Recently, Gradient-based post-training quantization (GPTQ) methods appears to be constitute a suitable trade-off between such simple methods and more powerful, yet expensive Quantization-Aware Training (QAT) approaches, particularly when attempting to quantize LLMs, where scalability of the quantization process is of paramount importance. GPTQ essentially consists in learning the rounding operation using a small calibration set. In this work, we challenge common choices in GPTQ methods. In particular, we show that the process is, to a certain extent, robust to a number of variables (weight selection, feature augmentation, choice of calibration set). More importantly, we derive a number of best practices for designing more efficient and scalable GPTQ methods, regarding the problem formulation (loss, degrees of freedom, use of non-uniform quantization schemes) or optimization process (choice of variable and optimizer). Lastly, we propose a novel importance-based mixed-precision technique. Those guidelines lead to significant performance improvements on all the tested state-of-the-art GPTQ methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving the way for the design of scalable, yet effective quantization methods.

Transformer-based large language models (LLMs) have achieved remarkable success as model sizes continue to grow, yet their deployment remains challenging due to significant computational and memory demands. Quantization has emerged as a promising solution, and state-of-the-art quantization algorithms for LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), where lower-precision weights are multiplied with higher-precision activations. Despite its benefits, current hardware accelerators such as GPUs and TPUs lack native support for efficient mpGEMM, leading to inefficient dequantization operations in the main sequential loop. To address this limitation, we introduce MixPE, a specialized mixed-precision processing element designed for efficient low-bit quantization in LLM inference. MixPE leverages two key innovations to minimize dequantization overhead and unlock the full potential of low-bit quantization. First, recognizing that scale and zero point are shared within each quantization group, we propose performing dequantization after per-group mpGEMM, significantly reducing dequantization overhead. Second, instead of relying on conventional multipliers, MixPE utilizes efficient shift\&add operations for multiplication, optimizing both computation and energy efficiency. Our experimental results demonstrate that MixPE surpasses the state-of-the-art quantization accelerators by 2.6times speedup and 1.4times energy reduction.

Quantization is an effective method for reducing memory footprint and inference time of Neural Networks, e.g., for efficient inference in the cloud, especially at the edge. However, ultra low precision quantization could lead to significant degradation in model generalization. A promising method to address this is to perform mixed-precision quantization, where more sensitive layers are kept at higher precision. However, the search space for a mixed-precision quantization is exponential in the number of layers. Recent work has proposed HAWQ, a novel Hessian based framework, with the aim of reducing this exponential search space by using second-order information. While promising, this prior work has three major limitations: (i) HAWQV1 only uses the top Hessian eigenvalue as a measure of sensitivity and do not consider the rest of the Hessian spectrum; (ii) HAWQV1 approach only provides relative sensitivity of different layers and therefore requires a manual selection of the mixed-precision setting; and (iii) HAWQV1 does not consider mixed-precision activation quantization. Here, we present HAWQV2 which addresses these shortcomings. For (i), we perform a theoretical analysis showing that a better sensitivity metric is to compute the average of all of the Hessian eigenvalues. For (ii), we develop a Pareto frontier based method for selecting the exact bit precision of different layers without any manual selection. For (iii), we extend the Hessian analysis to mixed-precision activation quantization. We have found this to be very beneficial for object detection. We show that HAWQV2 achieves new state-of-the-art results for a wide range of tasks.

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were developed over the centuries by mathematicians, who emphasized the attainability of arbitrary precision. Computers, however, operate on few limited precision types, such as the popular float32. In this study, we show that when aiming for limited precision, existing approximation methods can be outperformed by programs automatically discovered from scratch by a simple evolutionary algorithm. In particular, over real numbers, our method can approximate the exponential function reaching orders of magnitude more precision for a given number of operations when compared to previous approaches. More practically, over float32 numbers and constrained to less than 1 ULP of error, the same method attains a speedup over baselines by generating code that triggers better XLA/LLVM compilation paths. In other words, in both cases, evolution searched a vast space of possible programs, without knowledge of mathematics, to discover previously unknown optimized approximations to high precision, for the first time. We also give evidence that these results extend beyond the exponential. The ubiquity of transcendental functions suggests that our method has the potential to reduce the cost of scientific computing applications.

Quantization is a widely-used compression technology to reduce the overhead of serving large language models (LLMs) on terminal devices and in cloud data centers. However, prevalent quantization methods, such as 8-bit weight-activation or 4-bit weight-only quantization, achieve limited performance improvements due to poor support for low-precision (e.g., 4-bit) activation. This work, for the first time, realizes practical W4A4KV4 serving for LLMs, fully utilizing the INT4 tensor cores on modern GPUs and reducing the memory bottleneck caused by the KV cache. Specifically, we propose a novel fine-grained mixed-precision quantization algorithm (FMPQ) that compresses most activations into 4-bit with negligible accuracy loss. To support mixed-precision matrix multiplication for W4A4 and W4A8, we develop a highly optimized W4Ax kernel. Our approach introduces a novel mixed-precision data layout to facilitate access and fast dequantization for activation and weight tensors, utilizing the GPU's software pipeline to hide the overhead of data loading and conversion. Additionally, we propose fine-grained streaming multiprocessor (SM) scheduling to achieve load balance across different SMs. We integrate the optimized W4Ax kernel into our inference framework, COMET, and provide efficient management to support popular LLMs such as LLaMA-3-70B. Extensive evaluations demonstrate that, when running LLaMA family models on a single A100-80G-SMX4, COMET achieves a kernel-level speedup of 2.88times over cuBLAS and a 2.02 times throughput improvement compared to TensorRT-LLM from an end-to-end framework perspective.

Deploying neural networks on microcontroller units (MCUs) presents substantial challenges due to their constrained computation and memory resources. Previous researches have explored patch-based inference as a strategy to conserve memory without sacrificing model accuracy. However, this technique suffers from severe redundant computation overhead, leading to a substantial increase in execution latency. A feasible solution to address this issue is mixed-precision quantization, but it faces the challenges of accuracy degradation and a time-consuming search time. In this paper, we propose QuantMCU, a novel patch-based inference method that utilizes value-driven mixed-precision quantization to reduce redundant computation. We first utilize value-driven patch classification (VDPC) to maintain the model accuracy. VDPC classifies patches into two classes based on whether they contain outlier values. For patches containing outlier values, we apply 8-bit quantization to the feature maps on the dataflow branches that follow. In addition, for patches without outlier values, we utilize value-driven quantization search (VDQS) on the feature maps of their following dataflow branches to reduce search time. Specifically, VDQS introduces a novel quantization search metric that takes into account both computation and accuracy, and it employs entropy as an accuracy representation to avoid additional training. VDQS also adopts an iterative approach to determine the bitwidth of each feature map to further accelerate the search process. Experimental results on real-world MCU devices show that QuantMCU can reduce computation by 2.2x on average while maintaining comparable model accuracy compared to the state-of-the-art patch-based inference methods.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language modeling, generative networks and industrial recommendation systems. BFLOAT16 is attractive for Deep Learning training for two reasons: the range of values it can represent is the same as that of IEEE 754 floating-point format (FP32) and conversion to/from FP32 is simple. Maintaining the same range as FP32 is important to ensure that no hyper-parameter tuning is required for convergence; e.g., IEEE 754 compliant half-precision floating point (FP16) requires hyper-parameter tuning. In this paper, we discuss the flow of tensors and various key operations in mixed precision training, and delve into details of operations, such as the rounding modes for converting FP32 tensors to BFLOAT16. We have implemented a method to emulate BFLOAT16 operations in Tensorflow, Caffe2, IntelCaffe, and Neon for our experiments. Our results show that deep learning training using BFLOAT16 tensors achieves the same state-of-the-art (SOTA) results across domains as FP32 tensors in the same number of iterations and with no changes to hyper-parameters.

This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical evaluation across models ranging from 10M to 1B parameters, we demonstrate that quantization can achieve up to 68% reduction in model size while maintaining performance within 6% of full-precision baselines when utilizing our proposed scaling factor {\gamma}. Our experiments show that INT8 quantization delivers a 40% reduction in computational cost and power consumption, while INT4 quantization further improves these metrics by 60%. We introduce a novel theoretical framework for mixed-precision quantization, deriving optimal bit allocation strategies based on layer sensitivity and weight variance. Hardware efficiency evaluations on edge devices reveal that our quantization approach enables up to 2.4x throughput improvement for INT8 and 3x for INT4, with 60% power reduction compared to full-precision models.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point quantization and thus cannot well fit the LLM losses in this scenario. In contrast, while floating-point quantization training is more commonly implemented in production, the research on it has been relatively superficial. In this paper, we thoroughly explore the effects of floating-point quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in floating-point quantization training performance of LLM models. While presenting an accurate floating-point quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal floating-point quantization precision is directly proportional to the computational power, but within a wide computational power range, we estimate that the best cost-performance precision lies between 4-8 bits.

Current low-precision quantization algorithms often have the hidden cost of conversion back and forth from floating point to quantized integer values. This hidden cost limits the latency improvement realized by quantizing Neural Networks. To address this, we present HAWQV3, a novel mixed-precision integer-only quantization framework. The contributions of HAWQV3 are the following: (i) An integer-only inference where the entire computational graph is performed only with integer multiplication, addition, and bit shifting, without any floating point operations or even integer division; (ii) A novel hardware-aware mixed-precision quantization method where the bit-precision is calculated by solving an integer linear programming problem that balances the trade-off between model perturbation and other constraints, e.g., memory footprint and latency; (iii) Direct hardware deployment and open source contribution for 4-bit uniform/mixed-precision quantization in TVM, achieving an average speed up of 1.45times for uniform 4-bit, as compared to uniform 8-bit for ResNet50 on T4 GPUs; and (iv) extensive evaluation of the proposed methods on ResNet18/50 and InceptionV3, for various model compression levels with/without mixed precision. For ResNet50, our INT8 quantization achieves an accuracy of 77.58%, which is 2.68% higher than prior integer-only work, and our mixed-precision INT4/8 quantization can reduce INT8 latency by 23% and still achieve 76.73% accuracy. Our framework and the TVM implementation have been open sourced.

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ (Attention-aware Post-Training Mixed-Precision Quantization) for LLMs, which considers not only the second-order information of each layer's weights, but also, for the first time, the nonlinear effect of attention outputs on the entire model. We leverage the Hessian trace as a sensitivity metric for mixed-precision quantization, ensuring an informed precision reduction that retains model performance. Experiments show APTQ surpasses previous quantization methods, achieving an average of 4 bit width a 5.22 perplexity nearly equivalent to full precision in the C4 dataset. In addition, APTQ attains state-of-the-art zero-shot accuracy of 68.24\% and 70.48\% at an average bitwidth of 3.8 in LLaMa-7B and LLaMa-13B, respectively, demonstrating its effectiveness to produce high-quality quantized LLMs.

Quantization is a promising approach for reducing the inference time and memory footprint of neural networks. However, most existing quantization methods require access to the original training dataset for retraining during quantization. This is often not possible for applications with sensitive or proprietary data, e.g., due to privacy and security concerns. Existing zero-shot quantization methods use different heuristics to address this, but they result in poor performance, especially when quantizing to ultra-low precision. Here, we propose ZeroQ , a novel zero-shot quantization framework to address this. ZeroQ enables mixed-precision quantization without any access to the training or validation data. This is achieved by optimizing for a Distilled Dataset, which is engineered to match the statistics of batch normalization across different layers of the network. ZeroQ supports both uniform and mixed-precision quantization. For the latter, we introduce a novel Pareto frontier based method to automatically determine the mixed-precision bit setting for all layers, with no manual search involved. We extensively test our proposed method on a diverse set of models, including ResNet18/50/152, MobileNetV2, ShuffleNet, SqueezeNext, and InceptionV3 on ImageNet, as well as RetinaNet-ResNet50 on the Microsoft COCO dataset. In particular, we show that ZeroQ can achieve 1.71\% higher accuracy on MobileNetV2, as compared to the recently proposed DFQ method. Importantly, ZeroQ has a very low computational overhead, and it can finish the entire quantization process in less than 30s (0.5\% of one epoch training time of ResNet50 on ImageNet). We have open-sourced the ZeroQ frameworkhttps://github.com/amirgholami/ZeroQ.

The massive computational costs associated with large language model (LLM) pretraining have spurred great interest in reduced-precision floating-point representations to accelerate the process. As a result, the BrainFloat16 (BF16) precision has become the de facto standard for LLM training, with hardware support included in recent accelerators. This trend has gone even further in the latest processors, where FP8 has recently been introduced. However, prior experience with FP16, which was found to be less stable than BF16, raises concerns as to whether FP8, with even fewer bits than FP16, can be a cost-effective option for LLM training. We argue that reduced-precision training schemes must have similar training stability and hyperparameter sensitivities to their higher-precision counterparts in order to be cost-effective. However, we find that currently available methods for FP8 training are not robust enough to allow their use as economical replacements. This prompts us to investigate the stability of reduced-precision LLM training in terms of robustness across random seeds and learning rates. To this end, we propose new evaluation techniques and a new metric for quantifying loss landscape sharpness in autoregressive language models. By simulating incremental bit reductions in floating-point representations, we analyze the relationship between representational power and training stability with the intent of aiding future research into the field.

We introduce Mixtral 8x7B, a Sparse Mixture of Experts (SMoE) language model. Mixtral has the same architecture as Mistral 7B, with the difference that each layer is composed of 8 feedforward blocks (i.e. experts). For every token, at each layer, a router network selects two experts to process the current state and combine their outputs. Even though each token only sees two experts, the selected experts can be different at each timestep. As a result, each token has access to 47B parameters, but only uses 13B active parameters during inference. Mixtral was trained with a context size of 32k tokens and it outperforms or matches Llama 2 70B and GPT-3.5 across all evaluated benchmarks. In particular, Mixtral vastly outperforms Llama 2 70B on mathematics, code generation, and multilingual benchmarks. We also provide a model fine-tuned to follow instructions, Mixtral 8x7B - Instruct, that surpasses GPT-3.5 Turbo, Claude-2.1, Gemini Pro, and Llama 2 70B - chat model on human benchmarks. Both the base and instruct models are released under the Apache 2.0 license.

Gravitational waves from merging binary neutron stars carry characteristic information about their astrophysical properties, including masses and tidal deformabilities, that are needed to infer their radii. In this study, we use Bayesian inference to quantify the precision with which radius can inferred with upgrades in the current gravitational wave detectors and next-generation observatories such as the Einstein Telescope and Cosmic Explorer. We assign evidences for a set of plausible equations of state, which are then used as weights to obtain radius posteriors. We find that prior choices and the loudness of observed signals limit the precision and accuracy of inferred radii by current detectors. In contrast, next-generation observatories can resolve the radius precisely and accurately, across most of the mass range to within lesssim 5% for both soft and stiff equations of state. We also explore how the choice of the neutron star mass prior can influence the inferred masses and potentially affect radii measurements, finding that choosing an astrophysically motivated prior does not notably impact an individual neutron star's radius measurements.

Despite the popularity of guitar effects, there is very little existing research on classification and parameter estimation of specific plugins or effect units from guitar recordings. In this paper, convolutional neural networks were used for classification and parameter estimation for 13 overdrive, distortion and fuzz guitar effects. A novel dataset of processed electric guitar samples was assembled, with four sub-datasets consisting of monophonic or polyphonic samples and discrete or continuous settings values, for a total of about 250 hours of processed samples. Results were compared for networks trained and tested on the same or on a different sub-dataset. We found that discrete datasets could lead to equally high performance as continuous ones, whilst being easier to design, analyse and modify. Classification accuracy was above 80\%, with confusion matrices reflecting similarities in the effects timbre and circuits design. With parameter values between 0.0 and 1.0, the mean absolute error is in most cases below 0.05, while the root mean square error is below 0.1 in all cases but one.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

State-of-the-art space science missions increasingly rely on automation due to spacecraft complexity and the costs of human oversight. The high volume of data, including scientific and telemetry data, makes manual inspection challenging. Machine learning offers significant potential to meet these demands. The Euclid space telescope, in its survey phase since February 2024, exemplifies this shift. Euclid's success depends on accurate monitoring and interpretation of housekeeping telemetry and science-derived data. Thousands of telemetry parameters, monitored as time series, may or may not impact the quality of scientific data. These parameters have complex interdependencies, often due to physical relationships (e.g., proximity of temperature sensors). Optimising science operations requires careful anomaly detection and identification of hidden parameter states. Moreover, understanding the interactions between known anomalies and physical quantities is crucial yet complex, as related parameters may display anomalies with varied timing and intensity. We address these challenges by analysing temperature anomalies in Euclid's telemetry from February to August 2024, focusing on eleven temperature parameters and 35 covariates. We use a predictive XGBoost model to forecast temperatures based on historical values, detecting anomalies as deviations from predictions. A second XGBoost model predicts anomalies from covariates, capturing their relationships to temperature anomalies. We identify the top three anomalies per parameter and analyse their interactions with covariates using SHAP (Shapley Additive Explanations), enabling rapid, automated analysis of complex parameter relationships. Our method demonstrates how machine learning can enhance telemetry monitoring, offering scalable solutions for other missions with similar data challenges.

The optimal bit-width for achieving the best trade-off between quantized model size and accuracy has been a subject of ongoing debate. While some advocate for 4-bit quantization, others propose that 1.58-bit offers superior results. However, the lack of a cohesive framework for different bits has left such conclusions relatively tenuous. We present ParetoQ, the first unified framework that facilitates rigorous comparisons across 1-bit, 1.58-bit, 2-bit, 3-bit, and 4-bit quantization settings. Our findings reveal a notable learning transition between 2 and 3 bits: For 3-bits and above, the fine-tuned models stay close to their original pre-trained distributions, whereas for learning 2-bit networks or below, the representations change drastically. By optimizing training schemes and refining quantization functions, ParetoQ surpasses all previous methods tailored to specific bit widths. Remarkably, our ParetoQ ternary 600M-parameter model even outperforms the previous SoTA ternary 3B-parameter model in accuracy, using only one-fifth of the parameters. Extensive experimentation shows that ternary, 2-bit, and 3-bit quantization maintains comparable performance in the size-accuracy trade-off and generally exceeds 4-bit and binary quantization. Considering hardware constraints, 2-bit quantization offers promising potential for memory reduction and speedup.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

Quantization has become one of the most effective methodologies to compress LLMs into smaller size. However, the existing quantization solutions still show limitations of either non-negligible accuracy drop or system inefficiency. In this paper, we make a comprehensive analysis of the general quantization principles on their effect to the triangle of accuracy, memory consumption and system efficiency. We propose MixLLM that explores the new optimization space of mixed-precision quantization between output features based on the insight that different output features matter differently in the model. MixLLM identifies the output features with high salience in the global view rather than within each single layer, effectively assigning the larger bit-width to output features that need it most to achieve good accuracy with low memory consumption. We present the sweet spot of quantization configuration of algorithm-system co-design that leads to high accuracy and system efficiency. To address the system challenge, we design the two-step dequantization to make use of the int8 Tensor Core easily and fast data type conversion to reduce dequantization overhead significantly, and present the software pipeline to overlap the memory access, dequantization and the MatMul to the best. Extensive experiments show that with only 10% more bits, the PPL increasement can be reduced from about 0.5 in SOTA to within 0.2 for Llama 3.1 70B, while on average MMLU-Pro improves by 0.93 over the SOTA of three popular models. In addition to its superior accuracy, MixLLM also achieves state-of-the-art system efficiency.

Fine-tuning is a crucial process for adapting large language models (LLMs) to diverse applications. In certain scenarios, such as multi-tenant serving, deploying multiple LLMs becomes necessary to meet complex demands. Recent studies suggest decomposing a fine-tuned LLM into a base model and corresponding delta weights, which are then compressed using low-rank or low-bit approaches to reduce costs. In this work, we observe that existing low-rank and low-bit compression methods can significantly harm the model performance for task-specific fine-tuned LLMs (e.g., WizardMath for math problems). Motivated by the long-tail distribution of singular values in the delta weights, we propose a delta quantization approach using mixed-precision. This method employs higher-bit representation for singular vectors corresponding to larger singular values. We evaluate our approach on various fine-tuned LLMs, including math LLMs, code LLMs, chat LLMs, and even VLMs. Experimental results demonstrate that our approach performs comparably to full fine-tuned LLMs, surpassing both low-rank and low-bit baselines by a considerable margin. Additionally, we show that our method is compatible with various backbone LLMs, such as Llama-2, Llama-3, and Mistral, highlighting its generalizability.

We apply augmentations to our dataset to enhance the quality of our predictions and make our final models more resilient to noisy data and domain drifts. Yet the question remains, how are these augmentations going to perform with different hyper-parameters? In this study we evaluate the sensitivity of augmentations with regards to the model's hyper parameters along with their consistency and influence by performing a Local Surrogate (LIME) interpretation on the impact of hyper-parameters when different augmentations are applied to a machine learning model. We have utilized Linear regression coefficients for weighing each augmentation. Our research has proved that there are some augmentations which are highly sensitive to hyper-parameters and others which are more resilient and reliable.

The singlet-doublet vector-like fermion dark matter model has been extensively studied in the literature over the past decade. An important parameter in this model is the singlet-doublet mixing angle (sintheta). All the previous studies have primarily focused on annihilation and co-annihilation processes for obtaining the correct dark matter relic density, assuming that the singlet and doublet components decouple at the same epoch. In this work, we demonstrate that this assumption holds only for larger mixing angles with a dependency on the mass of the dark matter. However, it badly fails for the mixing angle sintheta<0.05. We present a systematic study of the parameter space of the singlet-doublet dark matter relic, incorporating annihilation, co-annihilation, and, for the first time, co-scattering processes. Additionally, the freeze-in parameter space is also explored. We found that due to the inclusion of co-scattering processes, the correct relic density parameter space is shifted towards the detection sensitivity range of the LHC and MATHUSLA via displaced vertex signatures.

When quantizing neural networks for efficient inference, low-bit integers are the go-to format for efficiency. However, low-bit floating point numbers have an extra degree of freedom, assigning some bits to work on an exponential scale instead. This paper in-depth investigates this benefit of the floating point format for neural network inference. We detail the choices that can be made for the FP8 format, including the important choice of the number of bits for the mantissa and exponent, and show analytically in which settings these choices give better performance. Then we show how these findings translate to real networks, provide an efficient implementation for FP8 simulation, and a new algorithm that enables the learning of both the scale parameters and the number of exponent bits in the FP8 format. Our chief conclusion is that when doing post-training quantization for a wide range of networks, the FP8 format is better than INT8 in terms of accuracy, and the choice of the number of exponent bits is driven by the severity of outliers in the network. We also conduct experiments with quantization-aware training where the difference in formats disappears as the network is trained to reduce the effect of outliers.

Post-training quantization is the leading method for addressing memory-related bottlenecks in LLM inference, but unfortunately, it suffers from significant performance degradation below 4-bit precision. An alternative approach involves training compressed models directly at a low bitwidth (e.g., binary or ternary models). However, the performance, training dynamics, and scaling trends of such models are not yet well understood. To address this issue, we train and openly release the Spectra LLM suite consisting of 54 language models ranging from 99M to 3.9B parameters, trained on 300B tokens. Spectra includes FloatLMs, post-training quantized QuantLMs (3, 4, 6, and 8 bits), and ternary LLMs (TriLMs) - our improved architecture for ternary language modeling, which significantly outperforms previously proposed ternary models of a given size (in bits), matching half-precision models at scale. For example, TriLM 3.9B is (bit-wise) smaller than the half-precision FloatLM 830M, but matches half-precision FloatLM 3.9B in commonsense reasoning and knowledge benchmarks. However, TriLM 3.9B is also as toxic and stereotyping as FloatLM 3.9B, a model six times larger in size. Additionally, TriLM 3.9B lags behind FloatLM in perplexity on validation splits and web-based corpora but performs better on less noisy datasets like Lambada and PennTreeBank. To enhance understanding of low-bitwidth models, we are releasing 500+ intermediate checkpoints of the Spectra suite at https://github.com/NolanoOrg/SpectraSuite{https://github.com/NolanoOrg/SpectraSuite}.

The softmax (also called softargmax) function is widely used in machine learning models to normalize real-valued scores into a probability distribution. To avoid floating-point overflow, the softmax function is conventionally implemented in three passes: the first pass to compute the normalization constant, and two other passes to compute outputs from normalized inputs. We analyze two variants of the Three-Pass algorithm and demonstrate that in a well-optimized implementation on HPC-class processors performance of all three passes is limited by memory bandwidth. We then present a novel algorithm for softmax computation in just two passes. The proposed Two-Pass algorithm avoids both numerical overflow and the extra normalization pass by employing an exotic representation for intermediate values, where each value is represented as a pair of floating-point numbers: one representing the "mantissa" and another representing the "exponent". Performance evaluation demonstrates that on out-of-cache inputs on an Intel Skylake-X processor the new Two-Pass algorithm outperforms the traditional Three-Pass algorithm by up to 28% in AVX512 implementation, and by up to 18% in AVX2 implementation. The proposed Two-Pass algorithm also outperforms the traditional Three-Pass algorithm on Intel Broadwell and AMD Zen 2 processors. To foster reproducibility, we released an open-source implementation of the new Two-Pass Softmax algorithm and other experiments in this paper as a part of XNNPACK library at GitHub.com/google/XNNPACK.

In this work, we aim to estimate the stellar parameters of the primary (Aa) by performing asteroseismic analysis on its period-spacing pattern. We use the C-3PO neural network to perform asteroseismic modelling of the g-mode period-spacing pattern of Aa, discussing the interplay of this information with external constraints from spectroscopy (T_{rm eff} and log(g)) and eclipse modelling (R). To estimate the level of uncertainty due to different frequency extraction and pattern identification processes, we consider four different variations on the period-spacing patterns. To better understand the correlations between and the uncertainty structure of our parameter estimates, we also employed a classical, parameter-based MCMC grid search on four different stellar grids. The best-fitting, externally constrained model to the period-spacing pattern arrives at estimates of the stellar properties for Aa of: M=1.51 pm 0.05 M_odot, X_c =0.43 pm 0.04, R=1.66 pm 0.1 R_odot, f_{rm ov}=0.010, Omega_c=1.58 pm 0.01 d^{-1} with rigid rotation to within the measurement errors, log(T_{rm eff})=3.856 pm 0.008 dex, log(g)=4.18 pm 0.04 dex, and log(L)=0.809 pm 0.005 dex, which agree well with previous measurements from eclipse modelling, spectroscopy, and the Gaia DR3 luminosity. We find that the near-core properties of the best-fitting asteroseismic models are consistent with external constraints from eclipse modelling and spectroscopy. Aa appears to be a typical example of a gamma Dor star, fitting well within existing populations. We find that Aa is quasi-rigidly rotating to within the uncertainties, and note that the asteroseismic age estimate for Aa (1100 pm 100 Myr) is considerably older than the young (35 Myr) age implied by previous isochrone fits to the B binary in the literature. Our MCMC parameter-based grid-search agrees well with our pattern-modelling approach.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that {4-bit} precision is almost universally optimal for total model bits and zero-shot accuracy.

Gravitational waves from asymmetric mass-ratio black-hole binaries carry unique information about their astrophysical environment. For instance, the Laser Interferometer Space Antenna (LISA) could potentially measure the amplitude and slope of gas torques in binaries embedded in the accretion disks of Active Galactic Nuclei, helping differentiate competing accretion disk models. However, this relies on simplified analytic models, which do not account for the stochastic variability of torques seen in hydrodynamic simulations. In this work, we use hydrodynamic simulations to create gravitational waveforms for extreme and intermediate mass-ratio inspirals in the LISA band. We then analyze these simulated waveforms using simpler templates that assume analytic torques, without stochastic time variability. By performing realistic Bayesian parameter estimation, we find no bias at 90% confidence in the binary parameters; however, estimates of accretion disk parameters, such as torque amplitude and slope, may be biased. Typically, the posterior distribution is centered around the average value of the torques, but when stochastic variability is large, the posterior can indicate no torques, even though they are present in the simulation. Our results suggest that while simplified analytic torque models work well for estimating binary parameters, caution is needed when using them to infer properties of the accretion disk. This work moves towards a more realistic assessment of one of the LISA science objectives, i.e., probing the properties of the astrophysical environments of black holes.

We analyze the parameter estimation accuracy that can be achieved for the mass and spin of SgrA*, the SMBH in our Galactic Center, by detecting multiple extremely large mass-ratio inspirals (XMRIs). XMRIs are formed by brown dwarfs (BD) inspiraling into a supermassive black hole (SMBH), thus emitting gravitational waves (GWs) inside the detection band of future space-based detectors such as LISA and TianQin. Theoretical estimates suggest the presence of approximately 10 XMRIs emitting detectable GWs, making them some of the most promising candidates for space-based GW detectors. Our analysis indicates that even if individual sources have low SNRs (approx10), high-precision parameter estimates can still be achieved by detecting multiple sources. In this case, the accuracy of the parameter estimates increases by approximately one to two orders of magnitude, at least. Moreover, by analyzing a small sample of 400 initial conditions for XMRIs formed in the Galactic Center, we estimate that almost 80 % of the detectable XMRIs orbiting SgrA* will have eccentricities between 0.43 to 0.95 and an SNRin [10,100]. The remaining sim20 % of the sources have an SNRin [100,1000] and eccentricities ranging from 0.25 to 0.92. Additionally, some XMRIs with high SNR are far from being circular. These loud sources with SNRapprox 1000 can have eccentricities as high as eapprox0.7; although their detection chances are low, representing lesssim2 % of the detectable sources, their presence is not ruled out.

In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation in spline interpolation, designed to meet user-defined precision requirements. Unlike traditional methods that rely on manually configured knot distributions with numerous parameters, the proposed technique automatically determines the optimal number and placement of knots based on interpolation error criteria. This simplifies configuration, often requiring only a single parameter. The algorithm progressively improves the interpolation by adaptively sampling the function-to-be-approximated, f(x), in regions where the interpolation error exceeds the desired threshold. All function evaluations contribute directly to the final approximation, ensuring efficiency. While each resampling step involves recomputing the interpolation table, this process is highly optimized and usually computationally negligible compared to the cost of evaluating f(x). We show the algorithm's efficacy through a series of precision tests on different functions. However, the study underscores the necessity for caution when dealing with certain function types, notably those featuring plateaus. To address this challenge, a heuristic enhancement is incorporated, improving accuracy in flat regions. This algorithm has been extensively used and tested over the years. NumCosmo includes a comprehensive set of unit tests that rigorously evaluate the algorithm both directly and indirectly, underscoring its robustness and reliability. As a practical application, we compute the surface mass density Sigma(R) and the average surface mass density Sigma(<R) for Navarro-Frenk-White and Hernquist halo density profiles, which provide analytical benchmarks. (abridged)

In this paper, we uncover that Language Models (LMs), either encoder- or decoder-based, can obtain new capabilities by assimilating the parameters of homologous models without retraining or GPUs. Typically, new abilities of LMs can be imparted by Supervised Fine-Tuning (SFT), reflected in the disparity between fine-tuned and pre-trained parameters (i.e., delta parameters). We initially observe that by introducing a novel operation called DARE (Drop And REscale), most delta parameters can be directly set to zeros without affecting the capabilities of SFT LMs and larger models can tolerate a higher proportion of discarded parameters. Based on this observation, we further sparsify delta parameters of multiple SFT homologous models with DARE and subsequently merge them into a single model by parameter averaging. We conduct experiments on eight datasets from the GLUE benchmark with BERT and RoBERTa. We also merge WizardLM, WizardMath, and Code Alpaca based on Llama 2. Experimental results show that: (1) The delta parameter value ranges for SFT models are typically small, often within 0.005, and DARE can eliminate 99% of them effortlessly. However, once the models are continuously pre-trained, the value ranges can grow to around 0.03, making DARE impractical. We have also tried to remove fine-tuned instead of delta parameters and find that a 10% reduction can lead to drastically decreased performance (even to 0). This highlights that SFT merely stimulates the abilities via delta parameters rather than injecting new abilities into LMs; (2) DARE can merge multiple task-specific LMs into one LM with diverse abilities. For instance, the merger of WizardLM and WizardMath improves the GSM8K zero-shot accuracy of WizardLM from 2.2 to 66.3, retaining its instruction-following ability while surpassing WizardMath's original 64.2 performance. Codes are available at https://github.com/yule-BUAA/MergeLM.

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

Math reasoning is a highly active area of Large Language Model (LLM) research because it is a hallmark of artificial intelligence. However, few works have explored how math reasoning is encoded within LLM parameters and if it is a skill that can be isolated within a model. Doing so could allow targeted intervention to improve math performance without altering non-math behavior and foster understanding of how models encode math reasoning. We introduce Math Neurosurgery (MathNeuro), a method for isolating math-specific parameters in LLMs using only forward passes. MathNeuro builds on existing work by using weights and activations to calculate parameter importance, but isolates math-specific parameters by removing those important for general language tasks. Pruning parameters MathNeuro identifies deletes a LLM's math reasoning ability without destroying its general language ability. Scaling these parameters by a small constant improves a pretrained or instruction-tuned LLM's performance by 4-17% on GSM8K while leaving non-math behavior unaltered. MathNeuro is also data efficient: most of its effectiveness holds when identifying math-specific parameters using a single sample. MathNeuro highlights the potential for future work to intervene on math-specific parameters.

Large Language Models (LLM) often needs to be Continual Pre-Trained (CPT) to obtain the unfamiliar language skill or adapt into new domains. The huge training cost of CPT often asks for cautious choice of key hyper-parameters such as the mixture ratio of extra language or domain corpus. However, there is no systematic study which bridge the gap between the optimal mixture ratio and the actual model performance, and the gap between experimental scaling law and the actual deployment in the full model size. In this paper, we perform CPT on Llama-3 8B and 70B to enhance its Chinese ability. We study the optimal correlation between the Additional Language Mixture Ratio (ALMR) and the Learning Rate (LR) on the 8B size which directly indicate the optimal experimental set up. By thorough choice of hyper-parameter, and subsequent fine-tuning, the model capability is improved not only on the Chinese-related benchmark, but also some specific domains including math, coding and emotional intelligence. We deploy the final 70B version of LLM on an real-life chat system which obtain satisfying performance.

We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard function (constant, increasing, decreasing, up-then-down, down-then-up), various common survival distributions (log-logistic, Burr type XII, Weibull, Gompertz), and includes defective distributions (i.e., cure models). This generality is achieved using four basic distributional parameters: two scale-type parameters and two shape parameters. Generalising to covariate dependence, the scale-type regression components correspond to accelerated failure time (AFT) and proportional hazards (PH) models. Therefore, this general formulation unifies the most popular survival models which allows us to consider the practical value of possible modelling choices for survival data. Furthermore, in line with our proposed flexible baseline distribution, we advocate the use of multi-parameter regression in which more than one distributional parameter depends on covariates - rather than the usual convention of having a single covariate-dependent (scale) parameter. While many choices are available, we suggest introducing covariates through just one or other of the two scale parameters, which covers AFT and PH models, in combination with a `power' shape parameter, which allows for more complex non-AFT/non-PH effects, while the other shape parameter remains covariate-independent, and handles automatic selection of the baseline distribution. We explore inferential issues in simulations, both with and without a covariate, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by investigating differences between treatment groups using data from a lung cancer study and a melanoma study. Censoring is accommodated throughout.

In this work, we obtain the error estimate of the rotation parameter beta from the core bounce phase of the characteristic gravitational wave signal of a rapidly rotating core collapse supernova (CCSN). We quantify the error with asymptotic expansions of the covariance of a Maximum Likelihood Estimator (MLE) in terms of inverse powers of Signal-Noise Ratio (SNR), this method has been previously applied to parameter estimation for compact binary coalescences. When the second order of this expansion is negligible, it indicates that the first order is a good approximation of the error that will have a matching filter approach when estimating beta. The analysis indicates that we should be able to resolve the presence of rotation for the galactic and nearby extragalactic progenitors. We show that the estimation error Delta beta can be as small as a few percent and is larger for small values of beta.

Machine learning models have recently found tremendous success in data-driven control systems. However, standard learning models often suffer from an accuracy-robustness trade-off, which is a limitation that must be overcome in the control of safety-critical systems that require both high performance and rigorous robustness guarantees. In this work, we build upon the recent "locally biased smoothing" method to develop classifiers that simultaneously inherit high accuracy from standard models and high robustness from robust models. Specifically, we extend locally biased smoothing to the multi-class setting, and then overcome its performance bottleneck by generalizing the formulation to "mix" the outputs of a standard neural network and a robust neural network. We prove that when the robustness of the robust base model is certifiable, within a closed-form ell_p radius, no alteration or attack on an input can result in misclassification of the mixed classifier; the proposed model inherits the certified robustness. Moreover, we use numerical experiments on the CIFAR-10 benchmark dataset to verify that the mixed model noticeably improves the accuracy-robustness trade-off.

Post-Training Quantization (PTQ) is a powerful technique for model compression, reducing the precision of neural networks without additional training overhead. Recent works have investigated adopting 8-bit floating-point quantization (FP8) in the context of PTQ for model inference. However, the exploration of floating-point formats smaller than 8 bits and their comparison with integer quantization remains relatively limited. In this work, we present minifloats, which are reduced-precision floating-point formats capable of further reducing the memory footprint, latency, and energy cost of a model while approaching full-precision model accuracy. Our work presents a novel PTQ design-space exploration, comparing minifloat and integer quantization schemes across a range of 3 to 8 bits for both weights and activations. We examine the applicability of various PTQ techniques to minifloats, including weight equalization, bias correction, SmoothQuant, gradient-based learned rounding, and the GPTQ method. Our experiments validate the effectiveness of low-precision minifloats when compared to their integer counterparts across a spectrum of accuracy-precision trade-offs on a set of reference deep learning vision workloads. Finally, we evaluate our results against an FPGA-based hardware cost model, showing that integer quantization often remains the Pareto-optimal option, given its relatively smaller hardware resource footprint.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

The emergence of accurate open large language models (LLMs) has led to a race towards quantization techniques for such models enabling execution on end-user devices. In this paper, we revisit the problem of "extreme" LLM compression--defined as targeting extremely low bit counts, such as 2 to 3 bits per parameter, from the point of view of classic methods in Multi-Codebook Quantization (MCQ). Our work builds on top of Additive Quantization, a classic algorithm from the MCQ family, and adapts it to the quantization of language models. The resulting algorithm advances the state-of-the-art in LLM compression, outperforming all recently-proposed techniques in terms of accuracy at a given compression budget. For instance, when compressing Llama 2 models to 2 bits per parameter, our algorithm quantizes the 7B model to 6.93 perplexity (a 1.29 improvement relative to the best prior work, and 1.81 points from FP16), the 13B model to 5.70 perplexity (a .36 improvement) and the 70B model to 3.94 perplexity (a .22 improvement) on WikiText2. We release our implementation of Additive Quantization for Language Models AQLM as a baseline to facilitate future research in LLM quantization.

We present 360Zhinao models with 7B parameter size and context lengths spanning 4K, 32K and 360K, all available at https://github.com/Qihoo360/360zhinao. For rapid development in pretraining, we establish a stable and sensitive ablation environment to evaluate and compare experiment runs with minimal model size. Under such guidance, we perfect our data cleaning and composition strategies to pretrain 360Zhinao-7B-Base on 3.4T tokens. We also mainly emphasize data during alignment, where we strive to balance quantity and quality with filtering and reformatting. With tailored data, 360Zhinao-7B's context window is easily extended to 32K and 360K. RMs and RLHF are trained following SFT and credibly applied to specific tasks. All together these contributions lead to 360Zhinao-7B's competitive performance among models of similar size.

Large language models (LLMs) have pushed the limits of natural language understanding and exhibited excellent problem-solving ability. Despite the great success, most existing open-source LLMs (\eg, LLaMA-2) are still far away from satisfactory for solving mathematical problem due to the complex reasoning procedures. To bridge this gap, we propose MetaMath, a fine-tuned language model that specializes in mathematical reasoning. Specifically, we start by bootstrapping mathematical questions by rewriting the question from multiple perspectives without extra knowledge, which results in a new dataset called {MetaMathQA}. Then we fine-tune the LLaMA-2 models on MetaMathQA. Experimental results on two popular benchmarks (\ie, GSM8K and MATH) for mathematical reasoning demonstrate that MetaMath outperforms a suite of open-source LLMs by a significant margin. Our MetaMath-7B model achieves 66.4% on GSM8K and 19.4% on MATH, exceeding the state-of-the-art models of the same size by 11.5% and 8.7%. Particularly, {MetaMath-70B} achieves an accuracy of 82.3% on {GSM8K}, slightly better than {GPT-3.5-Turbo}. We release the {MetaMathQA} dataset, the {MetaMath} models with different model sizes and the training code for public use.

Model quantization is widely applied for compressing and accelerating deep neural networks (DNNs). However, conventional Quantization-Aware Training (QAT) focuses on training DNNs with uniform bit-width. The bit-width settings vary across different hardware and transmission demands, which induces considerable training and storage costs. Hence, the scheme of one-shot joint training multiple precisions is proposed to address this issue. Previous works either store a larger FP32 model to switch between different precision models for higher accuracy or store a smaller INT8 model but compromise accuracy due to using shared quantization parameters. In this paper, we introduce the Double Rounding quantization method, which fully utilizes the quantized representation range to accomplish nearly lossless bit-switching while reducing storage by using the highest integer precision instead of full precision. Furthermore, we observe a competitive interference among different precisions during one-shot joint training, primarily due to inconsistent gradients of quantization scales during backward propagation. To tackle this problem, we propose an Adaptive Learning Rate Scaling (ALRS) technique that dynamically adapts learning rates for various precisions to optimize the training process. Additionally, we extend our Double Rounding to one-shot mixed precision training and develop a Hessian-Aware Stochastic Bit-switching (HASB) strategy. Experimental results on the ImageNet-1K classification demonstrate that our methods have enough advantages to state-of-the-art one-shot joint QAT in both multi-precision and mixed-precision. We also validate the feasibility of our method on detection and segmentation tasks, as well as on LLMs task. Our codes are available at https://github.com/haiduo/Double-Rounding.

We present BabyLlama-2, a 345 million parameter model distillation-pretrained from two teachers on a 10 million word corpus for the BabyLM competition. On BLiMP and SuperGLUE benchmarks, BabyLlama-2 outperforms baselines trained on both 10 and 100 million word datasets with the same data mix, as well as its teacher models. Through an extensive hyperparameter sweep, we demonstrate that the advantages of distillation cannot be attributed to suboptimal hyperparameter selection of the teachers. Our findings underscore the need for further investigation into distillation techniques, particularly in data-limited settings.

Large language models (LLMs) with hundreds of billions of parameters require powerful server-grade GPUs for inference, limiting their practical deployment. To address this challenge, we introduce the outlier-aware weight quantization (OWQ) method, which aims to minimize LLM's footprint through low-precision representation. OWQ prioritizes a small subset of structured weights sensitive to quantization, storing them in high-precision, while applying highly tuned quantization to the remaining dense weights. This sensitivity-aware mixed-precision scheme reduces the quantization error notably, and extensive experiments demonstrate that 3.1-bit models using OWQ perform comparably to 4-bit models optimized by OPTQ. Furthermore, OWQ incorporates a parameter-efficient fine-tuning for task-specific adaptation, called weak column tuning (WCT), enabling accurate task-specific LLM adaptation with minimal memory overhead in the optimized format. OWQ represents a notable advancement in the flexibility, efficiency, and practicality of LLM optimization literature. The source code is available at https://github.com/xvyaward/owq

Low-precision formats such as float8 have been introduced in machine learning accelerated hardware to improve computational efficiency for large language models training and inference. Nevertheless, adoption by the ML community has been slowed down by the complex, and sometimes brittle, techniques required to match higher precision training accuracy. In this work, we present Scalify, a end-to-end scale propagation paradigm for computational graphs, generalizing and formalizing existing tensor scaling methods. Experiment results show that Scalify supports out-of-the-box float8 matrix multiplication and gradients representation, as well as float16 optimizer state storage. Our JAX implementation of Scalify is open-sourced at https://github.com/graphcore-research/jax-scalify

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below O(10^{-5}) even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the training process into different stages, with each stage using a new network that is optimized to fit the residue from the previous stage. Across successive stages, the residue magnitudes decreases substantially and follows an inverse power-law relationship with the residue frequencies. The multi-stage neural networks effectively mitigate the spectral biases associated with regular neural networks, enabling them to capture the high frequency feature of target functions. We demonstrate that the prediction error from the multi-stage training for both regression problems and physics-informed neural networks can nearly reach the machine-precision O(10^{-16}) of double-floating point within a finite number of iterations. Such levels of accuracy are rarely attainable using single neural networks alone.

Instruction tuning large language models (LLMs) remains a challenging task, owing to the complexity of hyperparameter selection and the difficulty involved in evaluating the tuned models. To determine the optimal hyperparameters, an automatic, robust, and reliable evaluation benchmark is essential. However, establishing such a benchmark is not a trivial task due to the challenges associated with evaluation accuracy and privacy protection. In response to these challenges, we introduce a judge large language model, named PandaLM, which is trained to distinguish the superior model given several LLMs. PandaLM's focus extends beyond just the objective correctness of responses, which is the main focus of traditional evaluation datasets. It addresses vital subjective factors such as relative conciseness, clarity, adherence to instructions, comprehensiveness, and formality. To ensure the reliability of PandaLM, we collect a diverse human-annotated test dataset, where all contexts are generated by humans and labels are aligned with human preferences. Our results indicate that PandaLM-7B achieves 93.75% of GPT-3.5's evaluation ability and 88.28% of GPT-4's in terms of F1-score on our test dataset. PandaLM enables the evaluation of LLM to be fairer but with less cost, evidenced by significant improvements achieved by models tuned through PandaLM compared to their counterparts trained with default Alpaca's hyperparameters. In addition, PandaLM does not depend on API-based evaluations, thus avoiding potential data leakage. All resources of PandaLM are released at https://github.com/WeOpenML/PandaLM.

The growing computational demands of training large language models (LLMs) necessitate more efficient methods. Quantized training presents a promising solution by enabling low-bit arithmetic operations to reduce these costs. While FP8 precision has demonstrated feasibility, leveraging FP4 remains a challenge due to significant quantization errors and limited representational capacity. This work introduces the first FP4 training framework for LLMs, addressing these challenges with two key innovations: a differentiable quantization estimator for precise weight updates and an outlier clamping and compensation strategy to prevent activation collapse. To ensure stability, the framework integrates a mixed-precision training scheme and vector-wise quantization. Experimental results demonstrate that our FP4 framework achieves accuracy comparable to BF16 and FP8, with minimal degradation, scaling effectively to 13B-parameter LLMs trained on up to 100B tokens. With the emergence of next-generation hardware supporting FP4, our framework sets a foundation for efficient ultra-low precision training.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

We present an open-source database of superconducting quantum device designs that may be used as the starting point for customized devices. Each design can be generated programmatically using the open-source Qiskit Metal package, and simulated using finite-element electromagnetic solvers. We present a robust workflow for achieving high accuracy on design simulations. Many designs in the database are experimentally validated, showing excellent agreement between simulated and measured parameters. Our database includes a front-end interface that allows users to generate ``best-guess'' designs based on desired circuit parameters. This project lowers the barrier to entry for research groups seeking to make a new class of devices by providing them a well-characterized starting point from which to refine their designs.

We introduce phi-3-mini, a 3.8 billion parameter language model trained on 3.3 trillion tokens, whose overall performance, as measured by both academic benchmarks and internal testing, rivals that of models such as Mixtral 8x7B and GPT-3.5 (e.g., phi-3-mini achieves 69% on MMLU and 8.38 on MT-bench), despite being small enough to be deployed on a phone. The innovation lies entirely in our dataset for training, a scaled-up version of the one used for phi-2, composed of heavily filtered web data and synthetic data. The model is also further aligned for robustness, safety, and chat format. We also provide some initial parameter-scaling results with a 7B and 14B models trained for 4.8T tokens, called phi-3-small and phi-3-medium, both significantly more capable than phi-3-mini (e.g., respectively 75% and 78% on MMLU, and 8.7 and 8.9 on MT-bench).

We reanalyze the spectral lag data for GRB 160625B using frequentist inference in order to constrain the energy scale (E_{QG}) of Lorentz Invariance Violation (LIV). For this purpose, we use profile likelihood to deal with the astrophysical nuisance parameters. This is in contrast to Bayesian inference implemented in previous works, where marginalization was carried out over the nuisance parameters. We show that with profile likelihood, we do not find a global minimum for chi^2 as a function of E_{QG} below the Planck scale for both linear and quadratic models of LIV, whereas bounded credible intervals were previously obtained using Bayesian inference. Therefore, we can set one-sided lower limits in a straightforward manner. We find that E_{QG} geq 2.55 times 10^{16} GeV and E_{QG} geq 1.85 times 10^7 GeV at 95\% c.l., for linear and quadratic LIV, respectively. Therefore, this is the first proof-of-principles application of profile likelihood method to the analysis of GRB spectral lag data to constrain LIV.

In this work, we introduce a single parameter omega, to effectively control granularity in diffusion-based synthesis. This parameter is incorporated during the denoising steps of the diffusion model's reverse process. Our approach does not require model retraining, architectural modifications, or additional computational overhead during inference, yet enables precise control over the level of details in the generated outputs. Moreover, spatial masks or denoising schedules with varying omega values can be applied to achieve region-specific or timestep-specific granularity control. Prior knowledge of image composition from control signals or reference images further facilitates the creation of precise omega masks for granularity control on specific objects. To highlight the parameter's role in controlling subtle detail variations, the technique is named Omegance, combining "omega" and "nuance". Our method demonstrates impressive performance across various image and video synthesis tasks and is adaptable to advanced diffusion models. The code is available at https://github.com/itsmag11/Omegance.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

We propose LLM-FP4 for quantizing both weights and activations in large language models (LLMs) down to 4-bit floating-point values, in a post-training manner. Existing post-training quantization (PTQ) solutions are primarily integer-based and struggle with bit widths below 8 bits. Compared to integer quantization, floating-point (FP) quantization is more flexible and can better handle long-tail or bell-shaped distributions, and it has emerged as a default choice in many hardware platforms. One characteristic of FP quantization is that its performance largely depends on the choice of exponent bits and clipping range. In this regard, we construct a strong FP-PTQ baseline by searching for the optimal quantization parameters. Furthermore, we observe a high inter-channel variance and low intra-channel variance pattern in activation distributions, which adds activation quantization difficulty. We recognize this pattern to be consistent across a spectrum of transformer models designed for diverse tasks, such as LLMs, BERT, and Vision Transformer models. To tackle this, we propose per-channel activation quantization and show that these additional scaling factors can be reparameterized as exponential biases of weights, incurring a negligible cost. Our method, for the first time, can quantize both weights and activations in the LLaMA-13B to only 4-bit and achieves an average score of 63.1 on the common sense zero-shot reasoning tasks, which is only 5.8 lower than the full-precision model, significantly outperforming the previous state-of-the-art by 12.7 points. Code is available at: https://github.com/nbasyl/LLM-FP4.

Recent work has shown the immense potential of synthetically generated datasets for training large language models (LLMs), especially for acquiring targeted skills. Current large-scale math instruction tuning datasets such as MetaMathQA (Yu et al., 2024) and MAmmoTH (Yue et al., 2024) are constructed using outputs from closed-source LLMs with commercially restrictive licenses. A key reason limiting the use of open-source LLMs in these data generation pipelines has been the wide gap between the mathematical skills of the best closed-source LLMs, such as GPT-4, and the best open-source LLMs. Building on the recent progress in open-source LLMs, our proposed prompting novelty, and some brute-force scaling, we construct OpenMathInstruct-1, a math instruction tuning dataset with 1.8M problem-solution pairs. The dataset is constructed by synthesizing code-interpreter solutions for GSM8K and MATH, two popular math reasoning benchmarks, using the recently released and permissively licensed Mixtral model. Our best model, OpenMath-CodeLlama-70B, trained on a subset of OpenMathInstruct-1, achieves a score of 84.6% on GSM8K and 50.7% on MATH, which is competitive with the best gpt-distilled models. We release our code, models, and the OpenMathInstruct-1 dataset under a commercially permissive license.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.

An amplitude analysis of B^-rightarrow D^- D^0 K_S^0 decays is performed using proton-proton collision data, corresponding to an integrated luminosity of 9,fb^{-1}, collected with the LHCb detector at center-of-mass energies of 7, 8, and 13,Tekern -0.1em V. A resonant structure of spin-parity 0^+ is observed in the D^0 K_S^0 invariant-mass spectrum with a significance of 5.3,sigma. The mass and width of the state, modeled with a Breit-Wigner lineshape, are determined to be 2883pm11pm6,Mekern -0.1em V!/c^2 and 87_{-47}^{+22}pm6,Mekern -0.1em V respectively, where the first uncertainties are statistical and the second systematic. These properties and the quark content are consistent with those of the open-charm tetraquark state T_{cs 0}^{*}(2870)^0 observed previously in the D^+ K^- final state of the B^-rightarrow D^- D^+ K^- decay. This result confirms the existence of the T_{cs 0}^{*}(2870)^0 state in a new decay mode. The T_{cs1}^{*}(2900)^0 state, reported in the B^-rightarrow D^- D^+ K^- decay, is also searched for in the D^0 K_S^0 invariant-mass spectrum of the B^- rightarrow D^- D^0 K_S^0 decay, without finding evidence for it.

Adapter Tuning, which freezes the pretrained language models (PLMs) and only fine-tunes a few extra modules, becomes an appealing efficient alternative to the full model fine-tuning. Although computationally efficient, the recent Adapters often increase parameters (e.g. bottleneck dimension) for matching the performance of full model fine-tuning, which we argue goes against their original intention. In this work, we re-examine the parameter-efficiency of Adapters through the lens of network pruning (we name such plug-in concept as SparseAdapter) and find that SparseAdapter can achieve comparable or better performance than standard Adapters when the sparse ratio reaches up to 80\%. Based on our findings, we introduce an easy but effective setting ``Large-Sparse'' to improve the model capacity of Adapters under the same parameter budget. Experiments on five competitive Adapters upon three advanced PLMs show that with proper sparse method (e.g. SNIP) and ratio (e.g. 40\%) SparseAdapter can consistently outperform their corresponding counterpart. Encouragingly, with the Large-Sparse setting, we can obtain further appealing gains, even outperforming the full fine-tuning by a large margin. Our code will be released at: https://github.com/Shwai-He/SparseAdapter.

FP8 is a natural progression for accelerating deep learning training inference beyond the 16-bit formats common in modern processors. In this paper we propose an 8-bit floating point (FP8) binary interchange format consisting of two encodings - E4M3 (4-bit exponent and 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit mantissa). While E5M2 follows IEEE 754 conventions for representatio of special values, E4M3's dynamic range is extended by not representing infinities and having only one mantissa bit-pattern for NaNs. We demonstrate the efficacy of the FP8 format on a variety of image and language tasks, effectively matching the result quality achieved by 16-bit training sessions. Our study covers the main modern neural network architectures - CNNs, RNNs, and Transformer-based models, leaving all the hyperparameters unchanged from the 16-bit baseline training sessions. Our training experiments include large, up to 175B parameter, language models. We also examine FP8 post-training-quantization of language models trained using 16-bit formats that resisted fixed point int8 quantization.

While fine-tuning pretrained models has become common practice, these models often underperform outside their specific domains. Recently developed model merging techniques enable the direct integration of multiple models, each fine-tuned for distinct tasks, into a single model. This strategy promotes multitasking capabilities without requiring retraining on the original datasets. However, existing methods fall short in addressing potential conflicts and complex correlations between tasks, especially in parameter-level adjustments, posing a challenge in effectively balancing parameter competition across various tasks. This paper introduces an innovative technique named PCB-Merging (Parameter Competition Balancing), a lightweight and training-free technique that adjusts the coefficients of each parameter for effective model merging. PCB-Merging employs intra-balancing to gauge parameter significance within individual tasks and inter-balancing to assess parameter similarities across different tasks. Parameters with low importance scores are dropped, and the remaining ones are rescaled to form the final merged model. We assessed our approach in diverse merging scenarios, including cross-task, cross-domain, and cross-training configurations, as well as out-of-domain generalization. The experimental results reveal that our approach achieves substantial performance enhancements across multiple modalities, domains, model sizes, number of tasks, fine-tuning forms, and large language models, outperforming existing model merging methods. The code is publicly available at: https://github.com/duguodong7/pcb-merging.

The recently released GPT-4 Code Interpreter has demonstrated remarkable proficiency in solving challenging math problems, primarily attributed to its ability to seamlessly reason with natural language, generate code, execute code, and continue reasoning based on the execution output. In this paper, we present a method to fine-tune open-source language models, enabling them to use code for modeling and deriving math equations and, consequently, enhancing their mathematical reasoning abilities. We propose a method of generating novel and high-quality datasets with math problems and their code-based solutions, referred to as MathCodeInstruct. Each solution interleaves natural language, code, and execution results. We also introduce a customized supervised fine-tuning and inference approach. This approach yields the MathCoder models, a family of models capable of generating code-based solutions for solving challenging math problems. Impressively, the MathCoder models achieve state-of-the-art scores among open-source LLMs on the MATH (45.2%) and GSM8K (83.9%) datasets, substantially outperforming other open-source alternatives. Notably, the MathCoder model not only surpasses ChatGPT-3.5 and PaLM-2 on GSM8K and MATH but also outperforms GPT-4 on the competition-level MATH dataset. The dataset and models will be released at https://github.com/mathllm/MathCoder.

Storing open-source fine-tuned models separately introduces redundancy and increases response times in applications utilizing multiple models. Delta-parameter pruning (DPP), particularly the random drop and rescale (DARE) method proposed by Yu et al., addresses this by pruning the majority of delta parameters--the differences between fine-tuned and pre-trained model weights--while typically maintaining minimal performance loss. However, DARE fails when either the pruning rate or the magnitude of the delta parameters is large. We highlight two key reasons for this failure: (1) an excessively large rescaling factor as pruning rates increase, and (2) high mean and variance in the delta parameters. To push DARE's limits, we introduce DAREx (DARE the eXtreme), which features two algorithmic improvements: (1) DAREx-q, a rescaling factor modification that significantly boosts performance at high pruning rates (e.g., >30 % on COLA and SST2 for encoder models, with even greater gains in decoder models), and (2) DAREx-L2, which combines DARE with AdamR, an in-training method that applies appropriate delta regularization before DPP. We also demonstrate that DAREx-q can be seamlessly combined with vanilla parameter-efficient fine-tuning techniques like LoRA and can facilitate structural DPP. Additionally, we revisit the application of importance-based pruning techniques within DPP, demonstrating that they outperform random-based methods when delta parameters are large. Through this comprehensive study, we develop a pipeline for selecting the most appropriate DPP method under various practical scenarios.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

Language models of code (LMs) work well when the surrounding code in the vicinity of generation provides sufficient context. This is not true when it becomes necessary to use types or functionality defined in another module or library, especially those not seen during training. LMs suffer from limited awareness of such global context and end up hallucinating, e.g., using types defined in other files incorrectly. Recent work tries to overcome this issue by retrieving global information to augment the local context. However, this bloats the prompt or requires architecture modifications and additional training. Integrated development environments (IDEs) assist developers by bringing the global context at their fingertips using static analysis. We extend this assistance, enjoyed by developers, to the LMs. We propose a notion of monitors that use static analysis in the background to guide the decoding. Unlike a priori retrieval, static analysis is invoked iteratively during the entire decoding process, providing the most relevant suggestions on demand. We demonstrate the usefulness of our proposal by monitoring for type-consistent use of identifiers whenever an LM generates code for object dereference. To evaluate our approach, we curate PragmaticCode, a dataset of open-source projects with their development environments. On models of varying parameter scale, we show that monitor-guided decoding consistently improves the ability of an LM to not only generate identifiers that match the ground truth but also improves compilation rates and agreement with ground truth. We find that LMs with fewer parameters, when guided with our monitor, can outperform larger LMs. With monitor-guided decoding, SantaCoder-1.1B achieves better compilation rate and next-identifier match than the much larger text-davinci-003 model. The datasets and code will be released at https://aka.ms/monitors4codegen .

Modern foundation models rely heavily on using scaling laws to guide crucial training decisions. Researchers often extrapolate the optimal architecture and hyper parameters settings from smaller training runs by describing the relationship between, loss, or task performance, and scale. All components of this process vary, from the specific equation being fit, to the training setup, to the optimization method. Each of these factors may affect the fitted law, and therefore, the conclusions of a given study. We discuss discrepancies in the conclusions that several prior works reach, on questions such as the optimal token to parameter ratio. We augment this discussion with our own analysis of the critical impact that changes in specific details may effect in a scaling study, and the resulting altered conclusions. Additionally, we survey over 50 papers that study scaling trends: while 45 of these papers quantify these trends using a power law, most under-report crucial details needed to reproduce their findings. To mitigate this, we we propose a checklist for authors to consider while contributing to scaling law research.

Recently, considerable efforts have been directed towards compressing Large Language Models (LLMs), which showcase groundbreaking capabilities across diverse applications but entail significant deployment costs due to their large sizes. Meanwhile, much less attention has been given to mitigating the costs associated with deploying multiple LLMs of varying sizes despite its practical significance. Thus, this paper introduces any-precision LLM, extending the concept of any-precision DNN to LLMs. Addressing challenges in any-precision LLM, we propose a lightweight method for any-precision quantization of LLMs, leveraging a post-training quantization framework, and develop a specialized software engine for its efficient serving. As a result, our solution significantly reduces the high costs of deploying multiple, different-sized LLMs by overlaying LLMs quantized to varying bit-widths, such as 3, 4, ..., n bits, into a memory footprint comparable to a single n-bit LLM. All the supported LLMs with varying bit-widths demonstrate state-of-the-art model quality and inference throughput, proving itself to be a compelling option for deployment of multiple, different-sized LLMs. The source code will be publicly available soon.

The recent surge of open-source large language models (LLMs) enables developers to create AI-based solutions while maintaining control over aspects such as privacy and compliance, thereby providing governance and ownership of the model deployment process. To utilize these LLMs, inference engines are needed. These engines load the model's weights onto available resources, such as GPUs, and process queries to generate responses. The speed of inference, or performance, of the LLM, is critical for real-time applications, as it computes millions or billions of floating point operations per inference. Recently, advanced inference engines such as vLLM have emerged, incorporating novel mechanisms such as efficient memory management to achieve state-of-the-art performance. In this paper, we analyze the performance, particularly the throughput (tokens generated per unit of time), of 20 LLMs using two inference libraries: vLLM and HuggingFace's pipelines. We investigate how various hyperparameters, which developers must configure, influence inference performance. Our results reveal that throughput landscapes are irregular, with distinct peaks, highlighting the importance of hyperparameter optimization to achieve maximum performance. We also show that applying hyperparameter optimization when upgrading or downgrading the GPU model used for inference can improve throughput from HuggingFace pipelines by an average of 9.16% and 13.7%, respectively.

The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually tuning parameters, there is still a lot of untapped potential as the learned configuration is static, i.e., parameter settings remain fixed throughout the run. However, it has been shown that some algorithm parameters are best adjusted dynamically during execution, e.g., to adapt to the current part of the optimization landscape. Thus far, this is most commonly achieved through hand-crafted heuristics. A promising recent alternative is to automatically learn such dynamic parameter adaptation policies from data. In this article, we give the first comprehensive account of this new field of automated dynamic algorithm configuration (DAC), present a series of recent advances, and provide a solid foundation for future research in this field. Specifically, we (i) situate DAC in the broader historical context of AI research; (ii) formalize DAC as a computational problem; (iii) identify the methods used in prior-art to tackle this problem; (iv) conduct empirical case studies for using DAC in evolutionary optimization, AI planning, and machine learning.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Recently, the Muon optimizer based on matrix orthogonalization has demonstrated strong results in training small-scale language models, but the scalability to larger models has not been proven. We identify two crucial techniques for scaling up Muon: (1) adding weight decay and (2) carefully adjusting the per-parameter update scale. These techniques allow Muon to work out-of-the-box on large-scale training without the need of hyper-parameter tuning. Scaling law experiments indicate that Muon achieves sim!2times computational efficiency compared to AdamW with compute optimal training. Based on these improvements, we introduce Moonlight, a 3B/16B-parameter Mixture-of-Expert (MoE) model trained with 5.7T tokens using Muon. Our model improves the current Pareto frontier, achieving better performance with much fewer training FLOPs compared to prior models. We open-source our distributed Muon implementation that is memory optimal and communication efficient. We also release the pretrained, instruction-tuned, and intermediate checkpoints to support future research.

Recently, finetuning pretrained Vision-Language Models (VLMs) has been a prevailing paradigm for achieving state-of-the-art performance in Visual Question Answering (VQA). However, as VLMs scale, finetuning full model parameters for a given task in low-resource settings becomes computationally expensive, storage inefficient, and prone to overfitting. Current parameter-efficient tuning methods dramatically reduce the number of tunable parameters, but there still exists a significant performance gap with full finetuning. In this paper, we propose MixPHM, a redundancy-aware parameter-efficient tuning method that outperforms full finetuning in low-resource VQA. Specifically, MixPHM is a lightweight module implemented by multiple PHM-experts in a mixture-of-experts manner. To reduce parameter redundancy, MixPHM reparameterizes expert weights in a low-rank subspace and shares part of the weights inside and across experts. Moreover, based on a quantitative redundancy analysis for adapters, we propose Redundancy Regularization to reduce task-irrelevant redundancy while promoting task-relevant correlation in MixPHM representations. Experiments conducted on VQA v2, GQA, and OK-VQA demonstrate that MixPHM outperforms state-of-the-art parameter-efficient methods and is the only one consistently surpassing full finetuning.

The large number of parameters of some prominent language models, such as BERT, makes their fine-tuning on downstream tasks computationally intensive and energy hungry. Previously researchers were focused on lower bit-width integer data types for the forward propagation of language models to save memory and computation. As for the backward propagation, however, only 16-bit floating-point data type has been used for the fine-tuning of BERT. In this work, we use integer arithmetic for both forward and back propagation in the fine-tuning of BERT. We study the effects of varying the integer bit-width on the model's metric performance. Our integer fine-tuning uses integer arithmetic to perform forward propagation and gradient computation of linear, layer-norm, and embedding layers of BERT. We fine-tune BERT using our integer training method on SQuAD v1.1 and SQuAD v2., and GLUE benchmark. We demonstrate that metric performance of fine-tuning 16-bit integer BERT matches both 16-bit and 32-bit floating-point baselines. Furthermore, using the faster and more memory efficient 8-bit integer data type, integer fine-tuning of BERT loses an average of 3.1 points compared to the FP32 baseline.

Quantizing model weights is critical for reducing the communication and inference costs of large models. However, quantizing models -- especially to low precisions like int4 or int2 -- requires a trade-off in model quality; int2, in particular, is known to severely degrade model quality. Consequently, practitioners are often forced to maintain multiple models with different quantization levels or serve a single model that best satisfies the quality-latency trade-off. On the other hand, integer data types, such as int8, inherently possess a nested (Matryoshka) structure where smaller bit-width integers, like int4 or int2, are nested within the most significant bits. This paper proposes Matryoshka Quantization (MatQuant), a novel multi-scale quantization technique that addresses the challenge of needing multiple quantized models. It allows training and maintaining just one model, which can then be served at different precision levels. Furthermore, due to the co-training and co-distillation regularization provided by MatQuant, the int2 precision models extracted by MatQuant can be up to 10% more accurate than standard int2 quantization (using techniques like QAT or OmniQuant). This represents significant progress in model quantization, demonstrated by the fact that, with the same recipe, an int2 FFN-quantized Gemma-2 9B model is more accurate than an int8 FFN-quantized Gemma-2 2B model.

Quantization techniques can reduce the size of Deep Neural Networks and improve inference latency and throughput by taking advantage of high throughput integer instructions. In this paper we review the mathematical aspects of quantization parameters and evaluate their choices on a wide range of neural network models for different application domains, including vision, speech, and language. We focus on quantization techniques that are amenable to acceleration by processors with high-throughput integer math pipelines. We also present a workflow for 8-bit quantization that is able to maintain accuracy within 1% of the floating-point baseline on all networks studied, including models that are more difficult to quantize, such as MobileNets and BERT-large.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Data augmentation is becoming essential for improving regression performance in critical applications including manufacturing, climate prediction, and finance. Existing techniques for data augmentation largely focus on classification tasks and do not readily apply to regression tasks. In particular, the recent Mixup techniques for classification have succeeded in improving the model performance, which is reasonable due to the characteristics of the classification task, but has limitations in regression. We show that mixing examples that have large data distances using linear interpolations may have increasingly-negative effects on model performance. Our key idea is thus to limit the distances between examples that are mixed. We propose RegMix, a data augmentation framework for regression that learns for each example how many nearest neighbors it should be mixed with for the best model performance using a validation set. Our experiments conducted both on synthetic and real datasets show that RegMix outperforms state-of-the-art data augmentation baselines applicable to regression.

There has been significant interest in "extreme" compression of large language models (LLMs), i.e., to 1-2 bits per parameter, which allows such models to be executed efficiently on resource-constrained devices. Existing work focused on improved one-shot quantization techniques and weight representations; yet, purely post-training approaches are reaching diminishing returns in terms of the accuracy-vs-bit-width trade-off. State-of-the-art quantization methods such as QuIP# and AQLM include fine-tuning (part of) the compressed parameters over a limited amount of calibration data; however, such fine-tuning techniques over compressed weights often make exclusive use of straight-through estimators (STE), whose performance is not well-understood in this setting. In this work, we question the use of STE for extreme LLM compression, showing that it can be sub-optimal, and perform a systematic study of quantization-aware fine-tuning strategies for LLMs. We propose PV-Tuning - a representation-agnostic framework that generalizes and improves upon existing fine-tuning strategies, and provides convergence guarantees in restricted cases. On the practical side, when used for 1-2 bit vector quantization, PV-Tuning outperforms prior techniques for highly-performant models such as Llama and Mistral. Using PV-Tuning, we achieve the first Pareto-optimal quantization for Llama 2 family models at 2 bits per parameter.

Due to the high computational demands executing a rigorous comparison between hyperparameter optimization (HPO) methods is often cumbersome. The goal of this paper is to facilitate a better empirical evaluation of HPO methods by providing benchmarks that are cheap to evaluate, but still represent realistic use cases. We believe these benchmarks provide an easy and efficient way to conduct reproducible experiments for neural hyperparameter search. Our benchmarks consist of a large grid of configurations of a feed forward neural network on four different regression datasets including architectural hyperparameters and hyperparameters concerning the training pipeline. Based on this data, we performed an in-depth analysis to gain a better understanding of the properties of the optimization problem, as well as of the importance of different types of hyperparameters. Second, we exhaustively compared various different state-of-the-art methods from the hyperparameter optimization literature on these benchmarks in terms of performance and robustness.

We study the robust interpolation problem of arbitrary data distributions supported on a bounded space and propose a two-fold law of robustness. Robust interpolation refers to the problem of interpolating n noisy training data points in R^d by a Lipschitz function. Although this problem has been well understood when the samples are drawn from an isoperimetry distribution, much remains unknown concerning its performance under generic or even the worst-case distributions. We prove a Lipschitzness lower bound Omega(n/p) of the interpolating neural network with p parameters on arbitrary data distributions. With this result, we validate the law of robustness conjecture in prior work by Bubeck, Li, and Nagaraj on two-layer neural networks with polynomial weights. We then extend our result to arbitrary interpolating approximators and prove a Lipschitzness lower bound Omega(n^{1/d}) for robust interpolation. Our results demonstrate a two-fold law of robustness: i) we show the potential benefit of overparametrization for smooth data interpolation when n=poly(d), and ii) we disprove the potential existence of an O(1)-Lipschitz robust interpolating function when n=exp(omega(d)).

The approximation of Partial Differential Equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and flexibility in implementing various PDEs, PINNs often suffer from limited accuracy due to the spectral bias of Multi-Layer Perceptrons (MLPs), which struggle to effectively learn high-frequency and non-linear components. Recently, parametric mesh representations in combination with neural networks have been investigated as a promising approach to eliminate the inductive biases of neural networks. However, they usually require very high-resolution grids and a large number of collocation points to achieve high accuracy while avoiding overfitting issues. In addition, the fixed positions of the mesh parameters restrict their flexibility, making it challenging to accurately approximate complex PDEs. To overcome these limitations, we propose Physics-Informed Gaussians (PIGs), which combine feature embeddings using Gaussian functions with a lightweight neural network. Our approach uses trainable parameters for the mean and variance of each Gaussian, allowing for dynamic adjustment of their positions and shapes during training. This adaptability enables our model to optimally approximate PDE solutions, unlike models with fixed parameter positions. Furthermore, the proposed approach maintains the same optimization framework used in PINNs, allowing us to benefit from their excellent properties. Experimental results show the competitive performance of our model across various PDEs, demonstrating its potential as a robust tool for solving complex PDEs. Our project page is available at https://namgyukang.github.io/Physics-Informed-Gaussians/

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that extract information about errors to enable error correction: as higher measurement weights require higher implementation costs and introduce more errors, it is important in code design to optimize measurement weight. This underlies the surging interest in quantum low-density parity-check (qLDPC) codes, the study of which has primarily focused on the asymptotic (large-code-limit) properties. In this work, we introduce a versatile and computationally efficient approach to stabilizer code weight reduction based on reinforcement learning (RL), which produces new low-weight codes that substantially outperform the state of the art in practically relevant parameter regimes, extending significantly beyond previously accessible small distances. For example, our approach demonstrates savings in physical qubit overhead compared to existing results by 1 to 2 orders of magnitude for weight 6 codes and brings the overhead into a feasible range for near-future experiments. We also investigate the interplay between code parameters using our RL framework, offering new insights into the potential efficiency and power of practically viable coding strategies. Overall, our results demonstrate how RL can effectively advance the crucial yet challenging problem of quantum code discovery and thereby facilitate a faster path to the practical implementation of fault-tolerant quantum technologies.

We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson line in 4D {cal N}=4 super-Yang-Mills theory. We introduce an improved truncation scheme with an 'OPE tail' approximation and use it to reproduce the 'bootstrability' results of Cavagli\`a et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the first OPE-coefficient squared at 't Hooft coupling (4pi)^2, linear-functional methods with two sum rules from integrated correlators give the rigorous result 0.294014873 pm 4.88 cdot 10^{-8}, whereas our methods give with machine-precision computations 0.294014228 pm 6.77 cdot 10^{-7}. For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

The high cost of full-parameter fine-tuning (FFT) of Large Language Models (LLMs) has led to a series of parameter-efficient fine-tuning (PEFT) methods. However, it remains unclear which methods provide the best cost-performance trade-off at different model scales. We introduce Astraios, a suite of 28 instruction-tuned OctoCoder models using 7 tuning methods and 4 model sizes up to 16 billion parameters. Through investigations across 5 tasks and 8 different datasets encompassing both code comprehension and code generation tasks, we find that FFT generally leads to the best downstream performance across all scales, and PEFT methods differ significantly in their efficacy based on the model scale. LoRA usually offers the most favorable trade-off between cost and performance. Further investigation into the effects of these methods on both model robustness and code security reveals that larger models tend to demonstrate reduced robustness and less security. At last, we explore the relationships among updated parameters, cross-entropy loss, and task performance. We find that the tuning effectiveness observed in small models generalizes well to larger models, and the validation loss in instruction tuning can be a reliable indicator of overall downstream performance.

What makes a good Large Language Model (LLM)? That it performs well on the relevant benchmarks -- which hopefully measure, with some validity, the presence of capabilities that are also challenged in real application. But what makes the model perform well? What gives a model its abilities? We take a recently introduced type of benchmark that is meant to challenge capabilities in a goal-directed, agentive context through self-play of conversational games, and analyse how performance develops as a function of model characteristics like number of parameters, or type of training. We find that while there is a clear relationship between number of parameters and performance, there is still a wide spread of performance points within a given size bracket, which is to be accounted for by training parameters such as fine-tuning data quality and method. From a more practical angle, we also find a certain degree of unpredictability about performance across access methods, possible due to unexposed sampling parameters, and a, very welcome, performance stability against at least moderate weight quantisation during inference.

Large language models (LLMs) are rapidly increasing in size, with the number of parameters becoming a key factor in the success of many commercial models, such as ChatGPT, Claude, and Bard. Even the recently released publicly accessible models for commercial usage, such as Falcon and Llama2, come equipped with billions of parameters. This significant increase in the number of parameters makes deployment and operation very costly. The remarkable progress in the field of quantization for large neural networks in general and LLMs in particular, has made these models more accessible by enabling them to be deployed on consumer-grade GPUs. Quantized models generally demonstrate comparable performance levels to their unquantized base counterparts. Nonetheless, there exists a notable gap in our comprehensive understanding of how these quantized models respond to hyperparameters, such as temperature, max new tokens, and topk, particularly for next word prediction. The present analysis reveals that nf4 and fp4 are equally proficient 4-bit quantization techniques, characterized by similar attributes such as inference speed, memory consumption, and the quality of generated content. the study identifies nf4 as displaying greater resilience to temperature variations in the case of the llama2 series of models at lower temperature, while fp4 and fp4-dq proves to be a more suitable choice for falcon series of models. It is noteworthy that, in general, 4-bit quantized models of varying sizes exhibit higher sensitivity to temperature in the range of 0.5 to 0.8, unlike their unquantized counterparts. Additionally, int8 quantization is associated with significantly slower inference speeds, whereas unquantized bfloat16 models consistently yield the fastest inference speeds across models of all sizes.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

Post-training quantization (PTQ) is a neural network compression technique that converts a full-precision model into a quantized model using lower-precision data types. Although it can help reduce the size and computational cost of deep neural networks, it can also introduce quantization noise and reduce prediction accuracy, especially in extremely low-bit settings. How to determine the appropriate quantization parameters (e.g., scaling factors and rounding of weights) is the main problem facing now. Existing methods attempt to determine these parameters by minimize the distance between features before and after quantization, but such an approach only considers local information and may not result in the most optimal quantization parameters. We analyze this issue and ropose PD-Quant, a method that addresses this limitation by considering global information. It determines the quantization parameters by using the information of differences between network prediction before and after quantization. In addition, PD-Quant can alleviate the overfitting problem in PTQ caused by the small number of calibration sets by adjusting the distribution of activations. Experiments show that PD-Quant leads to better quantization parameters and improves the prediction accuracy of quantized models, especially in low-bit settings. For example, PD-Quant pushes the accuracy of ResNet-18 up to 53.14% and RegNetX-600MF up to 40.67% in weight 2-bit activation 2-bit. The code is released at https://github.com/hustvl/PD-Quant.

We train, for the first time, large language models using FP8 precision on datasets up to 2 trillion tokens -- a 20-fold increase over previous limits. Through these extended training runs, we uncover critical instabilities in FP8 training that were not observable in earlier works with shorter durations. We trace these instabilities to outlier amplification by the SwiGLU activation function. Interestingly, we show, both analytically and empirically, that this amplification happens only over prolonged training periods, and link it to a SwiGLU weight alignment process. To address this newly identified issue, we introduce Smooth-SwiGLU, a novel modification that ensures stable FP8 training without altering function behavior. We also demonstrate, for the first time, FP8 quantization of both Adam optimizer moments. Combining these innovations, we successfully train a 7B parameter model using FP8 precision on 256 Intel Gaudi2 accelerators, achieving on-par results with the BF16 baseline while delivering up to a sim 34 % throughput improvement.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these fine-grained error-correction methods can incur significant overhead for quantum algorithms of increasing complexity. We present a first step in achieving error correction at the level of quantum algorithms by combining a unified perspective on modern quantum algorithms via quantum signal processing (QSP). An error model of under- or over-rotation of the signal processing operator parameterized by epsilon < 1 is introduced. It is shown that while Pauli Z-errors are not recoverable without additional resources, Pauli X and Y errors can be arbitrarily suppressed by coherently appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP of length O(2^k c^{k^2} d) is sufficient to correct any length-d QSP with c unique phases to k^{th}-order in error epsilon. Allowing an additional assumption, a lower bound of Omega(cd) is shown, which is tight for k = 1, on the length of the recovery sequence. Our algorithmic-level error correction method is applied to Grover's fixed-point search algorithm as a demonstration.

Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor (kNN) based precision-recall metrics to break down the statistical distance into fidelity and diversity. While they provide an intuitive method, we thoroughly analyze these metrics and identify oversimplified assumptions and undesirable properties of kNN that result in unreliable evaluation, such as susceptibility to outliers and insensitivity to distributional changes. Thus, we propose novel metrics, P-precision and P-recall (PP\&PR), based on a probabilistic approach that address the problems. Through extensive investigations on toy experiments and state-of-the-art generative models, we show that our PP\&PR provide more reliable estimates for comparing fidelity and diversity than the existing metrics. The codes are available at https://github.com/kdst-team/Probablistic_precision_recall.

Large pre-trained models (LPMs), such as large language models, have become ubiquitous and are employed in many applications. These models are often adapted to a desired domain or downstream task through a fine-tuning stage. This paper proposes SQFT, an end-to-end solution for low-precision sparse parameter-efficient fine-tuning of LPMs, allowing for effective model manipulation in resource-constrained environments. Additionally, an innovative strategy enables the merging of sparse weights with low-rank adapters without losing sparsity and accuracy, overcoming the limitations of previous approaches. SQFT also addresses the challenge of having quantized weights and adapters with different numerical precisions, enabling merging in the desired numerical format without sacrificing accuracy. Multiple adaptation scenarios, models, and comprehensive sparsity levels demonstrate the effectiveness of SQFT. Models and code are available at https://github.com/IntelLabs/Hardware-Aware-Automated-Machine-Learning.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

Zipf's law appears in many application areas but does not have a closed form expression, which may make its use cumbersome. Since it coincides with the truncated version of the Zeta distribution, in this paper we propose three approximate closed form expressions for the truncated Zeta distribution, which may be employed for Zipf's law as well. The three approximations are based on the replacement of the sum occurring in Zipf's law with an integral, and are named respectively the integral approximation, the average integral approximation, and the trapezoidal approximation. While the first one is shown to be of little use, the trapezoidal approximation exhibits an error which is typically lower than 1\%, but is as low as 0.1\% for the range of values of the Zipf parameter below 1.

Post-merger gravitational wave echoes provide a unique opportunity to probe the near-horizon structure of astrophysical black holes, that may be modified due to non-perturbative quantum gravity phenomena. However, since the waveform is subject to large theoretical uncertainties, it is necessary to develop model-agnostic search methods for detecting echoes from observational data. A promising strategy is to identify the characteristic quasinormal modes (QNMs) associated with echoes, {\it in frequency space}, which complements existing searches of quasiperiodic pulses in time. In this study, we build upon our previous work targeting these modes by incorporating relative phase information to optimize the Bayesian search algorithm. Using a new phase-marginalized likelihood, the performance can be significantly improved for well-resolved QNMs. This enables an efficient model-agnostic search for QNMs of different shapes by using a simple search template. To demonstrate the robustness of the search algorithm, we construct four complementary benchmarks for the echo waveform that span a diverse range of different theoretical possibilities for the near-horizon structure. We then validate our Bayesian search algorithms by injecting the benchmark models into different realizations of Gaussian noise. Using two types of phase-marginalized likelihoods, we find that the search algorithm can efficiently detect the corresponding QNMs. Therefore, our search strategy provides a concrete Bayesian and model-agnostic approach to "quantum black hole seismology".

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams, and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter-nucleon and dark matter-electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

A sample of 60,410 bona fide optical quasars with astrometric proper motions in Gaia EDR3 and spectroscopic redshifts above 0.5 in an oval 8400 square degree area of the sky is constructed. Using orthogonal Zernike functions of polar coordinates, the proper motion fields are fitted in a weighted least-squares adjustment of the entire sample and of six equal bins of sorted redshifts. The overall fit with 37 Zernike functions reveals a statistically significant pattern, which is likely to be of instrumental origin. The main feature of this pattern is a chain of peaks and dips mostly in the R.A. component with an amplitude of 25~muas yr^{-1}. This field is subtracted from each of the six analogous fits for quasars grouped by redshifts covering the range 0.5 through 7.03, with median values 0.72, 1.00, 1.25, 1.52, 1.83, 2.34. The resulting residual patterns are noisier, with formal uncertainties up to 8~muas yr^{-1} in the central part of the area. We detect a single high-confidence Zernike term for R.A. proper motion components of quasars with redshifts around 1.52 representing a general gradient of 30 muas yr^{-1} over 150degr on the sky. We do not find any small- or medium-scale systemic variations of the residual proper motion field as functions of redshift above the 2.5,sigma significance level.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

As recently demonstrated, Deep Neural Networks (DNN), usually trained using single precision IEEE 754 floating point numbers (binary32), can also work using lower precision. Therefore, 16-bit and 8-bit compressed format have attracted considerable attention. In this paper, we focused on two families of formats that have already achieved interesting results in compressing binary32 numbers in machine learning applications, without sensible degradation of the accuracy: bfloat and posit. Even if 16-bit and 8-bit bfloat/posit are routinely used for reducing the storage of the weights/biases of trained DNNs, the inference still often happens on the 32-bit FPU of the CPU (especially if GPUs are not available). In this paper we propose a way to decompress a tensor of bfloat/posits just before computations, i.e., after the compressed operands have been loaded within the vector registers of a vector capable CPU, in order to save bandwidth usage and increase cache efficiency. Finally, we show the architectural parameters and considerations under which this solution is advantageous with respect to the uncompressed one.

This paper explores the limits of the current generation of large language models for program synthesis in general purpose programming languages. We evaluate a collection of such models (with between 244M and 137B parameters) on two new benchmarks, MBPP and MathQA-Python, in both the few-shot and fine-tuning regimes. Our benchmarks are designed to measure the ability of these models to synthesize short Python programs from natural language descriptions. The Mostly Basic Programming Problems (MBPP) dataset contains 974 programming tasks, designed to be solvable by entry-level programmers. The MathQA-Python dataset, a Python version of the MathQA benchmark, contains 23914 problems that evaluate the ability of the models to synthesize code from more complex text. On both datasets, we find that synthesis performance scales log-linearly with model size. Our largest models, even without finetuning on a code dataset, can synthesize solutions to 59.6 percent of the problems from MBPP using few-shot learning with a well-designed prompt. Fine-tuning on a held-out portion of the dataset improves performance by about 10 percentage points across most model sizes. On the MathQA-Python dataset, the largest fine-tuned model achieves 83.8 percent accuracy. Going further, we study the model's ability to engage in dialog about code, incorporating human feedback to improve its solutions. We find that natural language feedback from a human halves the error rate compared to the model's initial prediction. Additionally, we conduct an error analysis to shed light on where these models fall short and what types of programs are most difficult to generate. Finally, we explore the semantic grounding of these models by fine-tuning them to predict the results of program execution. We find that even our best models are generally unable to predict the output of a program given a specific input.

We introduce the Bittensor Language Model, called "BTLM-3B-8K", a new state-of-the-art 3 billion parameter open-source language model. BTLM-3B-8K was trained on 627B tokens from the SlimPajama dataset with a mixture of 2,048 and 8,192 context lengths. BTLM-3B-8K outperforms all existing 3B parameter models by 2-5.5% across downstream tasks. BTLM-3B-8K is even competitive with some 7B parameter models. Additionally, BTLM-3B-8K provides excellent long context performance, outperforming MPT-7B-8K and XGen-7B-8K on tasks up to 8,192 context length. We trained the model on a cleaned and deduplicated SlimPajama dataset; aggressively tuned the \textmu P hyperparameters and schedule; used ALiBi position embeddings; and adopted the SwiGLU nonlinearity. On Hugging Face, the most popular models have 7B parameters, indicating that users prefer the quality-size ratio of 7B models. Compacting the 7B parameter model to one with 3B parameters, with little performance impact, is an important milestone. BTLM-3B-8K needs only 3GB of memory with 4-bit precision and takes 2.5x less inference compute than 7B models, helping to open up access to a powerful language model on mobile and edge devices. BTLM-3B-8K is available under an Apache 2.0 license on Hugging Face: https://huggingface.co/cerebras/btlm-3b-8k-base.

Low precision training and inference affect both the quality and cost of language models, but current scaling laws do not account for this. In this work, we devise "precision-aware" scaling laws for both training and inference. We propose that training in lower precision reduces the model's "effective parameter count," allowing us to predict the additional loss incurred from training in low precision and post-train quantization. For inference, we find that the degradation introduced by post-training quantization increases as models are trained on more data, eventually making additional pretraining data actively harmful. For training, our scaling laws allow us to predict the loss of a model with different parts in different precisions, and suggest that training larger models in lower precision may be compute optimal. We unify the scaling laws for post and pretraining quantization to arrive at a single functional form that predicts degradation from training and inference in varied precisions. We fit on over 465 pretraining runs and validate our predictions on model sizes up to 1.7B parameters trained on up to 26B tokens.

A dynamical model based on a phenomenological charm quark-nucleon(c-N) potential v_{cN} and the Pomeron-exchange mechanism is constructed to investigate the J/Psi photo-production on the nucleon from threshold to invariant mass W=300 GeV. The J/Psi-N potential,V_{J/Psi N}(r),is constructed by folding v_{cN} into the wavefunction Phi_{J/Psi}(cc) of J/Psi within a Constituent Quark Model(CQM) of Ref.[43]. A photo-production amplitude is also generated by v_{cN} by a cc-loop integration over the gammarightarrow cc vertex function and Phi_{J/Psi}(cc). No commonly used Vector Meson Dominance assumption is used to define this photo-production amplitude which is needed to describe the data near the threshold. The potential v_{cN}(r) is parameterized in a form such that the predicted V_{J/Psi N}(r) at large distances has the same Yukawa potential form extracted from a Lattice QCD(LQCD) calculation of Ref.[18]. The parameters of v_{cN} are determined by fitting the total cross section data of JLab by performing calculations that include J/Psi-N final state interactions(FSI). The resulting differential cross sections are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near threshold region, allowing for sensitive testing of the predicted J/Psi-N scattering amplitudes. By imposing the constraints of J/Psi-N potential extracted from the LQCD calculation, we have obtained three J/Psi-N potentials which fit the JLab data equally well. The resulting J/Psi-N scattering lengths are in the range of a=(-0.05 fm sim -0.25 fm). With the determined v_{cN}(r) and the wavefunctions generated from the same CQM, the constructed model is used to predict the cross sections of photo-production of eta_c(1S) and Psi(2S) mesons for future experimental tests.

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

Mathematical word problem-solving has long been recognized as a complex task for small language models (SLMs). A recent study hypothesized that the smallest model size, needed to achieve over 80% accuracy on the GSM8K benchmark, is 34 billion parameters. To reach this level of performance with smaller models, researcher often train SLMs to generate Python code or use tools to help avoid calculation errors. Additionally, they employ ensembling, where outputs of up to 100 model runs are combined to arrive at a more accurate result. Result selection is done using consensus, majority vote or a separate a verifier model used in conjunction with the SLM. Ensembling provides a substantial boost in accuracy but at a significant cost increase with multiple calls to the model (e.g., Phi-GSM uses top-48 to boost the performance from 68.2 to 81.5). In this work, we present Orca-Math, a 7-billion-parameter SLM based on the Mistral-7B, which achieves 86.81% on GSM8k without the need for multiple model calls or the use of verifiers, code execution or any other external tools. Our approach has the following key elements: (1) A high quality synthetic dataset of 200K math problems created using a multi-agent setup where agents collaborate to create the data, (2) An iterative learning techniques that enables the SLM to practice solving problems, receive feedback on its solutions and learn from preference pairs incorporating the SLM solutions and the feedback. When trained with Supervised Fine-Tuning alone, Orca-Math achieves 81.50% on GSM8k pass@1 metric. With iterative preference learning, Orca-Math achieves 86.81% pass@1. Orca-Math surpasses the performance of significantly larger models such as LLAMA-2-70B, WizardMath-70B, Gemini-Pro, ChatGPT-3.5. It also significantly outperforms other smaller models while using much smaller data (hundreds of thousands vs. millions of problems).

Recent work found that LLMs are sensitive to a wide range of arbitrary prompt dimensions, including the type of delimiters, answer enumerators, instruction wording, and more. This throws into question popular single-prompt evaluation practices. We present DOVE (Dataset Of Variation Evaluation) a large-scale dataset containing prompt perturbations of various evaluation benchmarks. In contrast to previous work, we examine LLM sensitivity from an holistic perspective, and assess the joint effects of perturbations along various dimensions, resulting in thousands of perturbations per instance. We evaluate several model families against DOVE, leading to several findings, including efficient methods for choosing well-performing prompts, observing that few-shot examples reduce sensitivity, and identifying instances which are inherently hard across all perturbations. DOVE consists of more than 250M prompt perturbations and model outputs, which we make publicly available to spur a community-wide effort toward meaningful, robust, and efficient evaluation. Browse the data, contribute, and more: https://slab-nlp.github.io/DOVE/

Instruction fine-tuning pretrained LLMs for diverse downstream tasks has demonstrated remarkable success and has captured the interest of both academics and practitioners. To ensure such fine-tuned LLMs align with human preferences, techniques such as RLHF and DPO have emerged. At the same time, there is increasing interest in smaller parameter counts for models. In this work, using OpenLLaMA 3Bv2 as a base model, we describe the recipe used to fine-tune the OpenBezoar family of models. In this recipe: We first generate synthetic instruction fine-tuning data using an open and commercially non-restrictive instruction fine-tuned variant of the Falcon-40B model under three schemes based on: LaMini-LM, WizardLM/Evol-Instruct (with databricks-dolly-15k as a seed dataset) and Orca (with the Flan Collection as a seed dataset), then filter these generations using GPT-4 as a human proxy. We then perform cost-effective QLoRA-based supervised fine-tuning sequentially with each scheme. The resulting checkpoint is further fine-tuned with a subset of the HH-RLHF dataset to minimize distribution shift prior to using the DPO loss to obtain the final checkpoint. Evaluation is done with the LM Eval Harness tasks/metrics as well as on MT-Bench using the "LLM-as-a-judge" framework with Claude 2.1, with the finding that the final checkpoint, "OpenBezoar-HH-RLHF-DPO", demonstrates superior performance over many models at the 3B parameter scale, even outperforming the top model in one of the categories on the Huggingface Open LLM Leaderboard. We release "OpenBezoar-SFT", "OpenBezoar-HH-RLHF-SFT", "OpenBezoar-HH-RLHF-DPO" checkpoints, alongside our generated datasets on HuggingFace at https://huggingface.co/collections/SurgeGlobal/open-bezoar-6620a24923e12127e9e2b9cc and our codebase at https://bitbucket.org/paladinanalytics/workspace/projects/OP.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Large pre-trained language models have recently gained significant traction due to their improved performance on various down-stream tasks like text classification and question answering, requiring only few epochs of fine-tuning. However, their large model sizes often prohibit their applications on resource-constrained edge devices. Existing solutions of yielding parameter-efficient BERT models largely rely on compute-exhaustive training and fine-tuning. Moreover, they often rely on additional compute heavy models to mitigate the performance gap. In this paper, we present Sensi-BERT, a sensitivity driven efficient fine-tuning of BERT models that can take an off-the-shelf pre-trained BERT model and yield highly parameter-efficient models for downstream tasks. In particular, we perform sensitivity analysis to rank each individual parameter tensor, that then is used to trim them accordingly during fine-tuning for a given parameter or FLOPs budget. Our experiments show the efficacy of Sensi-BERT across different downstream tasks including MNLI, QQP, QNLI, SST-2 and SQuAD, showing better performance at similar or smaller parameter budget compared to various alternatives.

The introduction of 8-bit floating-point (FP8) computation units in modern AI accelerators has generated significant interest in FP8-based large language model (LLM) inference. Unlike 16-bit floating-point formats, FP8 in deep learning requires a shared scaling factor. Additionally, while E4M3 and E5M2 are well-defined at the individual value level, their scaling and accumulation methods remain unspecified and vary across hardware and software implementations. As a result, FP8 behaves more like a quantization format than a standard numeric representation. In this work, we provide the first comprehensive analysis of FP8 computation and acceleration on two AI accelerators: the NVIDIA H100 and Intel Gaudi 2. Our findings highlight that the Gaudi 2, by leveraging FP8, achieves higher throughput-to-power efficiency during LLM inference, offering valuable insights into the practical implications of FP8 adoption for datacenter-scale LLM serving.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

With the rapid growth in the use of fine-tuning for large language models (LLMs), optimizing fine-tuning while keeping inference efficient has become highly important. However, this is a challenging task as it requires improvements in all aspects, including inference speed, fine-tuning speed, memory consumption, and, most importantly, model quality. Previous studies have attempted to achieve this by combining quantization with fine-tuning, but they have failed to enhance all four aspects simultaneously. In this study, we propose a new lightweight technique called Quantization for Efficient Fine-Tuning (QEFT). QEFT accelerates both inference and fine-tuning, is supported by robust theoretical foundations, offers high flexibility, and maintains good hardware compatibility. Our extensive experiments demonstrate that QEFT matches the quality and versatility of full-precision parameter-efficient fine-tuning, while using fewer resources. Our code is available at https://github.com/xvyaward/qeft.

Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).

As large language model (LLM) inference demands ever-greater resources, there is a rapid growing trend of using low-bit weights to shrink memory usage and boost inference efficiency. However, these low-bit LLMs introduce the need for mixed-precision matrix multiplication (mpGEMM), which is a crucial yet under-explored operation that involves multiplying lower-precision weights with higher-precision activations. Unfortunately, current hardware does not natively support mpGEMM, resulting in indirect and inefficient dequantization-based implementations. To address the mpGEMM requirements in low-bit LLMs, we explored the lookup table (LUT)-based approach for mpGEMM. However, a conventional LUT implementation falls short of its potential. To fully harness the power of LUT-based mpGEMM, we introduce LUT Tensor Core, a software-hardware co-design optimized for low-bit LLM inference. Specifically, we introduce software-based operator fusion and table symmetrization techniques to optimize table precompute and table storage, respectively. Then, LUT Tensor Core proposes the hardware design featuring an elongated tiling shape design to enhance table reuse and a bit-serial design to support various precision combinations in mpGEMM. Moreover, we design an end-to-end compilation stack with new instructions for LUT-based mpGEMM, enabling efficient LLM compilation and optimizations. The evaluation on low-bit LLMs (e.g., BitNet, LLAMA) shows that LUT Tensor Core achieves more than a magnitude of improvements on both compute density and energy efficiency.

Mixture of Expert Tuning (MoE-Tuning) has effectively enhanced the performance of general MLLMs with fewer parameters, yet its application in resource-limited medical settings has not been fully explored. To address this gap, we developed MoE-TinyMed, a model tailored for medical applications that significantly lowers parameter demands. In evaluations on the VQA-RAD, SLAKE, and Path-VQA datasets, MoE-TinyMed outperformed LLaVA-Med in all Med-VQA closed settings with just 3.6B parameters. Additionally, a streamlined version with 2B parameters surpassed LLaVA-Med's performance in PathVQA, showcasing its effectiveness in resource-limited healthcare settings.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Kernelized Stein discrepancy (KSD) is a score-based discrepancy widely used in goodness-of-fit tests. It can be applied even when the target distribution has an unknown normalising factor, such as in Bayesian analysis. We show theoretically and empirically that the KSD test can suffer from low power when the target and the alternative distributions have the same well-separated modes but differ in mixing proportions. We propose to perturb the observed sample via Markov transition kernels, with respect to which the target distribution is invariant. This allows us to then employ the KSD test on the perturbed sample. We provide numerical evidence that with suitably chosen transition kernels the proposed approach can lead to substantially higher power than the KSD test.

One of the current goals of neutrino experiments is to precisely determine standard unknown oscillation parameters such as the leptonic CP phase and mass hierarchy. Lorentz invariance violation represents a potential physics factor that could influence the experiment's ability to achieve these precise determinations. This study investigates the influence of Lorentz invariance violation (LIV) on oscillation dynamics, particularly through non-isotropic CPT-violating (a^{X}_{emu}, a^{X}_{etau}, a^{X}_{mutau}) and CPT-conserving (c^{XY}_{emu}, c^{XY}_{e tau}, c^{XY}_{mu tau}) parameters within the Deep Underground Neutrino Experiment (DUNE). We analyze the impact of these parameters on the mass hierarchy (MH) and Dirac CP phase sensitivity measurements. Our findings indicate that while MH sensitivity remains relatively unaffected, only the presence of c^{XY}_{mu tau} significantly deteriorates MH sensitivity, albeit remaining above the 5 sigma threshold. Additionally, we observe a substantial compromise in CP sensitivity due to the c^{XY}_{e mu} and c^{XY}_{e tau} parameters.

Here we present 1701 light curves of 1550 spectroscopically confirmed Type Ia supernovae (SNe Ia) that will be used to infer cosmological parameters as part of the Pantheon+ SN analysis and the SH0ES (Supernovae and H0 for the Equation of State of dark energy) distance-ladder analysis. This effort is one part of a series of works that perform an extensive review of redshifts, peculiar velocities, photometric calibration, and intrinsic-scatter models of SNe Ia. The total number of light curves, which are compiled across 18 different surveys, is a significant increase from the first Pantheon analysis (1048 SNe), particularly at low redshift (z). Furthermore, unlike in the Pantheon analysis, we include light curves for SNe with z<0.01 such that SN systematic covariance can be included in a joint measurement of the Hubble constant (H_0) and the dark energy equation-of-state parameter (w). We use the large sample to compare properties of 151 SNe Ia observed by multiple surveys and 12 pairs/triplets of "SN siblings" - SNe found in the same host galaxy. Distance measurements, application of bias corrections, and inference of cosmological parameters are discussed in the companion paper by Brout et al. (2022b), and the determination of H_0 is discussed by Riess et al. (2022). These analyses will measure w with sim3% precision and H_0 with 1 km/s/Mpc precision.

Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. However, quantization down to 3-4 bits per parameter usually leads to moderate-to-high accuracy losses, especially for smaller models in the 1-10B parameter range, which are well-suited for edge deployments. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique which enables for the first time near-lossless compression of LLMs across model scales, while reaching similar compression levels to previous methods. SpQR works by identifying and isolating outlier weights, which cause particularly-large quantization errors, and storing them in higher precision, while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than 1% in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run 33B parameter LLM on a single 24 GB consumer GPU without any performance degradation at 15% speedup thus making powerful LLMs available to consumer without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR which yields faster inference than 16-bit baselines at similar accuracy, while enabling memory compression gains of more than 4x.

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

In mixtures-of-experts (ME) model, where a number of submodels (experts) are combined, there have been two longstanding problems: (i) how many experts should be chosen, given the size of the training data? (ii) given the total number of parameters, is it better to use a few very complex experts, or is it better to combine many simple experts? In this paper, we try to provide some insights to these problems through a theoretic study on a ME structure where m experts are mixed, with each expert being related to a polynomial regression model of order k. We study the convergence rate of the maximum likelihood estimator (MLE), in terms of how fast the Kullback-Leibler divergence of the estimated density converges to the true density, when the sample size n increases. The convergence rate is found to be dependent on both m and k, and certain choices of m and k are found to produce optimal convergence rates. Therefore, these results shed light on the two aforementioned important problems: on how to choose m, and on how m and k should be compromised, for achieving good convergence rates.

We present a generic framework for creating differentially private versions of any hypothesis test in a black-box way. We analyze the resulting tests analytically and experimentally. Most crucially, we show good practical performance for small data sets, showing that at epsilon = 1 we only need 5-6 times as much data as in the fully public setting. We compare our work to the one existing framework of this type, as well as to several individually-designed private hypothesis tests. Our framework is higher power than other generic solutions and at least competitive with (and often better than) individually-designed tests.

Large Language Models (LLMs) have proven their exceptional capabilities in performing language-related tasks. However, their deployment poses significant challenges due to their considerable memory and storage requirements. In response to this issue, weight-only quantization, particularly 3 and 4-bit weight-only quantization, has emerged as one of the most viable solutions. As the number of bits decreases, the quantization grid broadens, thus emphasizing the importance of up and down rounding. While previous studies have demonstrated that fine-tuning up and down rounding with the addition of perturbations can enhance accuracy in some scenarios, our study is driven by the precise and limited boundary of these perturbations, where only the threshold for altering the rounding value is of significance. Consequently, we propose a concise and highly effective approach for optimizing the weight rounding task. Our method, named SignRound, involves lightweight block-wise tuning using signed gradient descent, enabling us to achieve outstanding results within 400 steps. SignRound outperforms the established baseline of rounding-to-nearest (RTN) and competes impressively against recent methods, without introducing additional inference overhead. The source code will be publicly available at https://github.com/intel/neural-compressor soon.

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity multiplication L-Mul algorithm that approximates floating point number multiplication with integer addition operations. The new algorithm costs significantly less computation resource than 8-bit floating point multiplication but achieves higher precision. Compared to 8-bit floating point multiplications, the proposed method achieves higher precision but consumes significantly less bit-level computation. Since multiplying floating point numbers requires substantially higher energy compared to integer addition operations, applying the L-Mul operation in tensor processing hardware can potentially reduce 95% energy cost by element-wise floating point tensor multiplications and 80% energy cost of dot products. We calculated the theoretical error expectation of L-Mul, and evaluated the algorithm on a wide range of textual, visual, and symbolic tasks, including natural language understanding, structural reasoning, mathematics, and commonsense question answering. Our numerical analysis experiments agree with the theoretical error estimation, which indicates that L-Mul with 4-bit mantissa achieves comparable precision as float8_e4m3 multiplications, and L-Mul with 3-bit mantissa outperforms float8_e5m2. Evaluation results on popular benchmarks show that directly applying L-Mul to the attention mechanism is almost lossless. We further show that replacing all floating point multiplications with 3-bit mantissa L-Mul in a transformer model achieves equivalent precision as using float8_e4m3 as accumulation precision in both fine-tuning and inference.

Large Mixture of Experts (MoE) models could achieve state-of-the-art quality on various language tasks, including machine translation task, thanks to the efficient model scaling capability with expert parallelism. However, it has brought a fundamental issue of larger memory consumption and increased memory bandwidth bottleneck at deployment time. In this paper, we propose Mixture of Quantized Experts (MoQE) which is a simple weight-only quantization method applying ultra low-bit down to 2-bit quantizations only to expert weights for mitigating the increased memory and latency issues of MoE models. We show that low-bit quantization together with the MoE architecture delivers a reliable model performance while reducing the memory size significantly even without any additional training in most cases. In particular, expert layers in MoE models are much more robust to the quantization than conventional feedforward networks (FFN) layers. In our comprehensive analysis, we show that MoE models with 2-bit expert weights can deliver better model performance than the dense model trained on the same dataset. As a result of low-bit quantization, we show the model size can be reduced by 79.6% of the original half precision floating point (fp16) MoE model. Combined with an optimized GPU runtime implementation, it also achieves 1.24X speed-up on A100 GPUs.

We introduce miniCTX, which tests a model's ability to prove formal mathematical theorems that depend on new definitions, lemmas, or other contextual information that was not observed during training. miniCTX contains theorems sourced from real Lean projects and textbooks, each associated with a context that can span tens of thousands of tokens. Models are tasked with proving a theorem given access to code from the theorem's repository, which contains context that is helpful or needed for the proof. As a baseline for miniCTX, we introduce file-tuning, a simple recipe that trains a model to generate a proof step conditioned on the preceding file contents. File-tuning substantially outperforms the traditional neural theorem proving approach that fine-tunes on states alone. Additionally, our file-tuned model improves performance on the standard miniF2F benchmark, achieving a pass rate of 33.61%, which is a new state-of-the-art for 1.3B parameter models. Alongside miniCTX, we offer ntp-toolkit for automatically extracting and annotating theorem proving data, making it easy to add new projects into miniCTX to ensure that contexts are not seen during training. miniCTX offers a challenging and realistic perspective on evaluating neural theorem provers.

Decoding methods play an indispensable role in converting language models from next-token predictors into practical task solvers. Prior research on decoding methods, primarily focusing on task-specific models, may not extend to the current era of general-purpose large language models (LLMs). Moreover, the recent influx of decoding strategies has further complicated this landscape. This paper provides a comprehensive and multifaceted analysis of various decoding methods within the context of LLMs, evaluating their performance, robustness to hyperparameter changes, and decoding speeds across a wide range of tasks, models, and deployment environments. Our findings reveal that decoding method performance is notably task-dependent and influenced by factors such as alignment, model size, and quantization. Intriguingly, sensitivity analysis exposes that certain methods achieve superior performance at the cost of extensive hyperparameter tuning, highlighting the trade-off between attaining optimal results and the practicality of implementation in varying contexts.

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values for them are proposed. Also, we propose an alternative to moving average. To compare the performance of the Gravity optimizer with two common optimizers, Adam and RMSProp, five standard datasets were trained on two VGGNet models with a batch size of 128 for 100 epochs. Gravity hyper-parameters did not need to be tuned for different models. As will be explained more in the paper, to investigate the direct impact of the optimizer itself on loss reduction no overfitting prevention technique was used. The obtained results show that the Gravity optimizer has more stable performance than Adam and RMSProp and gives greater values of validation accuracy for datasets with more output classes like CIFAR-100 (Fine).

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Despite the recent advances in the field of computational Schr\"odinger Bridges (SB), most existing SB solvers are still heavy-weighted and require complex optimization of several neural networks. It turns out that there is no principal solver which plays the role of simple-yet-effective baseline for SB just like, e.g., k-means method in clustering, logistic regression in classification or Sinkhorn algorithm in discrete optimal transport. We address this issue and propose a novel fast and simple SB solver. Our development is a smart combination of two ideas which recently appeared in the field: (a) parameterization of the Schr\"odinger potentials with sum-exp quadratic functions and (b) viewing the log-Schr\"odinger potentials as the energy functions. We show that combined together these ideas yield a lightweight, simulation-free and theoretically justified SB solver with a simple straightforward optimization objective. As a result, it allows solving SB in moderate dimensions in a matter of minutes on CPU without a painful hyperparameter selection. Our light solver resembles the Gaussian mixture model which is widely used for density estimation. Inspired by this similarity, we also prove an important theoretical result showing that our light solver is a universal approximator of SBs. Furthemore, we conduct the analysis of the generalization error of our light solver. The code for our solver can be found at https://github.com/ngushchin/LightSB

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-m rate, where m is the number of simulated samples. This can lead to significant computational challenges since a large m is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

Large Language Models (LLMs) are difficult to fully fine-tune (e.g., with instructions or human feedback) due to their sheer number of parameters. A family of parameter-efficient sparse fine-tuning (SFT) methods have proven promising in terms of performance but their memory requirements increase proportionally to the size of the LLMs. In this work, we scale sparse fine-tuning to state-of-the-art LLMs like LLaMA 2 7B and 13B. At any given time, for a desired density level, we maintain an array of parameter indices and the deltas of these parameters relative to their pretrained values. We iterate among: (a) updating the active deltas, (b) pruning indices (based on the change of magnitude of their deltas) and (c) regrowth of indices. For regrowth, we explore two criteria based on either the accumulated gradients of a few candidate parameters or their approximate momenta estimated using the efficient SM3 optimizer. We experiment with instruction-tuning of LLMs on standard dataset mixtures, finding that SFT is often superior to popular parameter-efficient fine-tuning methods like LoRA (low-rank adaptation) in terms of performance and comparable in terms of run time. We additionally show that SFT is compatible with both quantization and efficient optimizers, to facilitate scaling to ever-larger model sizes. We release the code for SFT at https://github.com/AlanAnsell/peft and for the instruction-tuning experiments at https://github.com/ducdauge/sft-llm.

The Mixture of Experts (MoE) is a widely known neural architecture where an ensemble of specialized sub-models optimizes overall performance with a constant computational cost. However, conventional MoEs pose challenges at scale due to the need to store all experts in memory. In this paper, we push MoE to the limit. We propose extremely parameter-efficient MoE by uniquely combining MoE architecture with lightweight experts.Our MoE architecture outperforms standard parameter-efficient fine-tuning (PEFT) methods and is on par with full fine-tuning by only updating the lightweight experts -- less than 1% of an 11B parameters model. Furthermore, our method generalizes to unseen tasks as it does not depend on any prior task knowledge. Our research underscores the versatility of the mixture of experts architecture, showcasing its ability to deliver robust performance even when subjected to rigorous parameter constraints. Our code used in all the experiments is publicly available here: https://github.com/for-ai/parameter-efficient-moe.

The Languini Kitchen serves as both a research collective and codebase designed to empower researchers with limited computational resources to contribute meaningfully to the field of language modelling. We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. The number of tokens on which a model is trained is defined by the model's throughput and the chosen compute class. Notably, this approach avoids constraints on critical hyperparameters which affect total parameters or floating-point operations. For evaluation, we pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. On it, we compare methods based on their empirical scaling trends which are estimated through experiments at various levels of compute. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput. While the GPT baseline achieves better perplexity throughout all our levels of compute, our LSTM baseline exhibits a predictable and more favourable scaling law. This is due to the improved throughput and the need for fewer training tokens to achieve the same decrease in test perplexity. Extrapolating the scaling laws leads of both models results in an intersection at roughly 50,000 accelerator hours. We hope this work can serve as the foundation for meaningful and reproducible language modelling research.

This paper presents Safurai-001, a new Large Language Model (LLM) with significant potential in the domain of coding assistance. Driven by recent advancements in coding LLMs, Safurai-001 competes in performance with the latest models like WizardCoder [Xu et al., 2023], PanguCoder [Shen et al., 2023] and Phi-1 [Gunasekar et al., 2023] but aims to deliver a more conversational interaction. By capitalizing on the progress in data engineering (including latest techniques of data transformation and prompt engineering) and instruction tuning, this new model promises to stand toe-to-toe with recent closed and open source developments. Recognizing the need for an efficacious evaluation metric for coding LLMs, this paper also introduces GPT4-based MultiParameters, an evaluation benchmark that harnesses varied parameters to present a comprehensive insight into the models functioning and performance. Our assessment shows that Safurai-001 can outperform GPT-3.5 by 1.58% and WizardCoder by 18.78% in the Code Readability parameter and more.

The Neural Arithmetic Logic Unit (NALU) is a neural network layer that can learn exact arithmetic operations between the elements of a hidden state. The goal of NALU is to learn perfect extrapolation, which requires learning the exact underlying logic of an unknown arithmetic problem. Evaluating the performance of the NALU is non-trivial as one arithmetic problem might have many solutions. As a consequence, single-instance MSE has been used to evaluate and compare performance between models. However, it can be hard to interpret what magnitude of MSE represents a correct solution and models sensitivity to initialization. We propose using a success-criterion to measure if and when a model converges. Using a success-criterion we can summarize success-rate over many initialization seeds and calculate confidence intervals. We contribute a generalized version of the previous arithmetic benchmark to measure models sensitivity under different conditions. This is, to our knowledge, the first extensive evaluation with respect to convergence of the NALU and its sub-units. Using a success-criterion to summarize 4800 experiments we find that consistently learning arithmetic extrapolation is challenging, in particular for multiplication.

Population Based Training (PBT) is an efficient hyperparameter optimization algorithm. PBT is a single-objective algorithm, but many real-world hyperparameter optimization problems involve two or more conflicting objectives. In this work, we therefore introduce a multi-objective version of PBT, MO-PBT. Our experiments on diverse multi-objective hyperparameter optimization problems (Precision/Recall, Accuracy/Fairness, Accuracy/Adversarial Robustness) show that MO-PBT outperforms random search, single-objective PBT, and the state-of-the-art multi-objective hyperparameter optimization algorithm MO-ASHA.

This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter tau to better than 15% (in combination with with the other low- and high-ell likelihoods). We also update the 2015 baseline low-ell joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker tau constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the LambdaCDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-ell implementations, we estimate the consistency of the results to be better than the 0.5sigma level. Minor curiosities already present before (differences between ell<800 and ell>800 parameters or the preference for more smoothing of the C_ell peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged)

Various parameter-efficient fine-tuning (PEFT) techniques have been proposed to enable computationally efficient fine-tuning while maintaining model performance. However, existing PEFT methods are still limited by the growing number of trainable parameters with the rapid deployment of Large Language Models (LLMs). To address this challenge, we present LoRETTA, an ultra-parameter-efficient framework that significantly reduces trainable parameters through tensor-train decomposition. Specifically, we propose two methods, named {LoRETTA}_{adp} and {LoRETTA}_{rep}. The former employs tensorized adapters, offering a high-performance yet lightweight approach for the fine-tuning of LLMs. The latter emphasizes fine-tuning via weight parameterization with a set of small tensor factors. LoRETTA achieves comparable or better performance than most widely used PEFT methods with up to 100times fewer parameters on the LLaMA-2-7B models. Furthermore, empirical results demonstrate that the proposed method effectively improves training efficiency, enjoys better multi-task learning performance, and enhances the anti-overfitting capability. Plug-and-play codes built upon the Huggingface framework and PEFT library will be released.

Recent work has identified simple empirical scaling laws for language models, linking compute budget, dataset size, model size, and autoregressive modeling loss. The validity of these simple power laws across orders of magnitude in model scale provides compelling evidence that larger models are also more capable models. However, scaling up models under the constraints of hardware and infrastructure is no easy feat, and rapidly becomes a hard and expensive engineering problem. We investigate ways to tentatively cheat scaling laws, and train larger models for cheaper. We emulate an increase in effective parameters, using efficient approximations: either by doping the models with frozen random parameters, or by using fast structured transforms in place of dense linear layers. We find that the scaling relationship between test loss and compute depends only on the actual number of trainable parameters; scaling laws cannot be deceived by spurious parameters.

Large language models (LLMs) with enormous pre-training tokens and parameter amounts emerge abilities, including math reasoning, code generation, and instruction following. These abilities are further enhanced by supervised fine-tuning (SFT). The open-source community has studied on ad-hoc SFT for each ability, while proprietary LLMs are versatile for all abilities. It is important to investigate how to unlock them with multiple abilities via SFT. In this study, we specifically focus on the data composition between mathematical reasoning, code generation, and general human-aligning abilities during SFT. From a scaling perspective, we investigate the relationship between model abilities and various factors including data amounts, data composition ratio, model parameters, and SFT strategies. Our experiments reveal that different abilities exhibit different scaling patterns, and larger models generally show superior performance with the same amount of data. Mathematical reasoning and code generation improve as data amounts increase consistently, while the general ability is enhanced with about a thousand samples and improves slowly. We find data composition results in various abilities improvements with low data amounts, while conflicts of abilities with high data amounts. Our experiments further show that composition data amount impacts performance, while the influence of composition ratio is insignificant. Regarding the SFT strategies, we evaluate sequential learning multiple abilities are prone to catastrophic forgetting. Our proposed Dual-stage Mixed Fine-tuning (DMT) strategy learns specialized abilities first and then learns general abilities with a small amount of specialized data to prevent forgetting, offering a promising solution to learn multiple abilities with different scaling patterns.

Pretraining data of large language models composes multiple domains (e.g., web texts, academic papers, codes), whose mixture proportions crucially impact the competence of outcome models. While existing endeavors rely on heuristics or qualitative strategies to tune the proportions, we discover the quantitative predictability of model performance regarding the mixture proportions in function forms, which we refer to as the data mixing laws. Fitting such functions on sample mixtures unveils model performance on unseen mixtures before actual runs, thus guiding the selection of an ideal data mixture. Furthermore, we propose nested use of the scaling laws of training steps, model sizes, and our data mixing law to enable predicting the performance of large models trained on massive data under various mixtures with only small-scale training. Moreover, experimental results verify that our method effectively optimizes the training mixture of a 1B model trained for 100B tokens in RedPajama, reaching a performance comparable to the one trained for 48% more steps on the default mixture. Extending the application of data mixing laws to continual training accurately predicts the critical mixture proportion that avoids catastrophic forgetting and outlooks the potential for dynamic data schedules

Adapting large-scale pretrained language models to downstream tasks via fine-tuning is the standard method for achieving state-of-the-art performance on NLP benchmarks. However, fine-tuning all weights of models with millions or billions of parameters is sample-inefficient, unstable in low-resource settings, and wasteful as it requires storing a separate copy of the model for each task. Recent work has developed parameter-efficient fine-tuning methods, but these approaches either still require a relatively large number of parameters or underperform standard fine-tuning. In this work, we propose Compacter, a method for fine-tuning large-scale language models with a better trade-off between task performance and the number of trainable parameters than prior work. Compacter accomplishes this by building on top of ideas from adapters, low-rank optimization, and parameterized hypercomplex multiplication layers. Specifically, Compacter inserts task-specific weight matrices into a pretrained model's weights, which are computed efficiently as a sum of Kronecker products between shared "slow" weights and "fast" rank-one matrices defined per Compacter layer. By only training 0.047% of a pretrained model's parameters, Compacter performs on par with standard fine-tuning on GLUE and outperforms standard fine-tuning on SuperGLUE and low-resource settings. Our code is publicly available at~https://github.com/rabeehk/compacter.

Recently, the idea of using FP8 as a number format for neural network training has been floating around the deep learning world. Given that most training is currently conducted with entire networks in FP32, or sometimes FP16 with mixed-precision, the step to having some parts of a network run in FP8 with 8-bit weights is an appealing potential speed-up for the generally costly and time-intensive training procedures in deep learning. A natural question arises regarding what this development means for efficient inference on edge devices. In the efficient inference device world, workloads are frequently executed in INT8. Sometimes going even as low as INT4 when efficiency calls for it. In this whitepaper, we compare the performance for both the FP8 and INT formats for efficient on-device inference. We theoretically show the difference between the INT and FP formats for neural networks and present a plethora of post-training quantization and quantization-aware-training results to show how this theory translates to practice. We also provide a hardware analysis showing that the FP formats are somewhere between 50-180% less efficient in terms of compute in dedicated hardware than the INT format. Based on our research and a read of the research field, we conclude that although the proposed FP8 format could be good for training, the results for inference do not warrant a dedicated implementation of FP8 in favor of INT8 for efficient inference. We show that our results are mostly consistent with previous findings but that important comparisons between the formats have thus far been lacking. Finally, we discuss what happens when FP8-trained networks are converted to INT8 and conclude with a brief discussion on the most efficient way for on-device deployment and an extensive suite of INT8 results for many models.

Parameter efficient finetuning has emerged as a viable solution for improving the performance of Large Language Models without requiring massive resources and compute. Prior work on multilingual evaluation has shown that there is a large gap between the performance of LLMs on English and other languages. Further, there is also a large gap between the performance of smaller open-source models and larger LLMs. Finetuning can be an effective way to bridge this gap and make language models more equitable. In this work, we finetune the LLaMA-7B and Mistral-7B models on synthetic multilingual instruction tuning data to determine its effect on model performance on five downstream tasks covering twenty three languages in all. Additionally, we experiment with various parameters, such as rank for low-rank adaptation and values of quantisation to determine their effects on downstream performance and find that higher rank and higher quantisation values benefit low-resource languages. We find that parameter efficient finetuning of smaller open source models sometimes bridges the gap between the performance of these models and the larger ones, however, English performance can take a hit. We also find that finetuning sometimes improves performance on low-resource languages, while degrading performance on high-resource languages.

Many problems in astrophysics cover multiple orders of magnitude in spatial and temporal scales. While simulating systems that experience rapid changes in these conditions, it is essential to adapt the (time-) step size to capture the behavior of the system during those rapid changes and use a less accurate time step at other, less demanding, moments. We encounter three problems with traditional methods. Firstly, making such changes requires expert knowledge of the astrophysics as well as of the details of the numerical implementation. Secondly, some parameters that determine the time-step size are fixed throughout the simulation, which means that they do not adapt to the rapidly changing conditions of the problem. Lastly, we would like the choice of time-step size to balance accuracy and computation effort. We address these challenges with Reinforcement Learning by training it to select the time-step size dynamically. We use the integration of a system of three equal-mass bodies that move due to their mutual gravity as an example of its application. With our method, the selected integration parameter adapts to the specific requirements of the problem, both in terms of computation time and accuracy while eliminating the expert knowledge needed to set up these simulations. Our method produces results competitive to existing methods and improve the results found with the most commonly-used values of time-step parameter. This method can be applied to other integrators without further retraining. We show that this extrapolation works for variable time-step integrators but does not perform to the desired accuracy for fixed time-step integrators.

We present constraints on the spacetime variation of the fine-structure constant alpha at redshifts 2.5le z<9.5 using JWST emission-line galaxies. The galaxy sample consists of 621 high-quality spectra with strong and narrow [O III] lambdalambda4959,5007 doublet emission lines from 578 galaxies, including 232 spectra at z>5. The [O III] doublet lines are arguably the best emission lines to probe the variation in alpha. We divide our sample into six subsamples based on redshift and calculate the relative variation Deltaalpha/alpha for the individual subsamples. The calculated Deltaalpha/alpha values are consistent with zero within 1sigma at all redshifts, suggesting no time variation in alpha above a level of (1-2) times10^{-4} (1sigma) in the past 13.2 billion years. When the whole sample is combined, the constraint is improved to be Deltaalpha/alpha = (0.2pm0.7) times10^{-4}. We further test the spatial variation in alpha using four subsamples of galaxies in four different directions on the sky. The measured Deltaalpha/alpha values are consistent with zero at a 1sigma level of sim 2times10^{-4}. While the constraints in this work are not as stringent as those from lower-redshift quasar absorption lines in previous studies, this work uses an independent tracer and provides the first constraints on Deltaalpha/alpha at the highest redshifts. With the growing number of emission-line galaxies from JWST, we expect to achieve stronger constraints in the future.

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences. It is the first time that the errors of a tsunami code have been assessed in this manner. To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.

We present the Chinese Elementary School Math Word Problems (CMATH) dataset, comprising 1.7k elementary school-level math word problems with detailed annotations, source from actual Chinese workbooks and exams. This dataset aims to provide a benchmark tool for assessing the following question: to what grade level of elementary school math do the abilities of popular large language models (LLMs) correspond? We evaluate a variety of popular LLMs, including both commercial and open-source options, and discover that only GPT-4 achieves success (accuracy geq 60\%) across all six elementary school grades, while other models falter at different grade levels. Furthermore, we assess the robustness of several top-performing LLMs by augmenting the original problems in the CMATH dataset with distracting information. Our findings reveal that GPT-4 is able to maintains robustness, while other model fail. We anticipate that our study will expose limitations in LLMs' arithmetic and reasoning capabilities, and promote their ongoing development and advancement.

While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized (e.g., 4-bit, or binary) counterparts, massive savings in computation cost, memory, and power consumption are attained. To that end, we generalize a post-training neural-network quantization method, GPFQ, that is based on a greedy path-following mechanism. Among other things, we propose modifications to promote sparsity of the weights, and rigorously analyze the associated error. Additionally, our error analysis expands the results of previous work on GPFQ to handle general quantization alphabets, showing that for quantizing a single-layer network, the relative square error essentially decays linearly in the number of weights -- i.e., level of over-parametrization. Our result holds across a range of input distributions and for both fully-connected and convolutional architectures thereby also extending previous results. To empirically evaluate the method, we quantize several common architectures with few bits per weight, and test them on ImageNet, showing only minor loss of accuracy compared to unquantized models. We also demonstrate that standard modifications, such as bias correction and mixed precision quantization, further improve accuracy.

Narrow bit-width data formats are key to reducing the computational and storage costs of modern deep learning applications. This paper evaluates Microscaling (MX) data formats that combine a per-block scaling factor with narrow floating-point and integer types for individual elements.MX formats balance the competing needs of hardware efficiency, model accuracy, and user friction. Empirical results on over two dozen benchmarks demonstrate practicality of MX data formats as a drop-in replacement for baseline FP32 for AI inference and training with low user friction. We also show the first instance of training generative language models at sub-8-bit weights, activations, and gradients with minimal accuracy loss and no modifications to the training recipe.

Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs. However, existing methods for large-scale dataset creation require substantial seed data and high computational costs for data synthesis, posing significant challenges for scalability. We introduce InfinityMATH, a scalable instruction tuning dataset for programmatic mathematical reasoning. The construction pipeline emphasizes decoupling numbers from mathematical problems to synthesize number-independent programs, enabling efficient and flexible scaling while minimizing dependency on specific numerical values. Fine-tuning experiments with open-source language and code models, such as Llama2 and CodeLlama, demonstrate the practical benefits of InfinityMATH. These fine-tuned models, showed significant relative improvements on both in-domain and out-of-domain benchmarks, ranging from 184.7% to 514.3% on average. Additionally, these models exhibited high robustness on the GSM8K+ and MATH+ benchmarks, which are enhanced version of test sets with simply the number variations. InfinityMATH ensures that models are more versatile and effective across a broader range of mathematical problems. The data is available at https://huggingface.co/datasets/flagopen/InfinityMATH.

The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well-established, yet their effective deployment necessitates careful hyperparameter optimization. Through extensive empirical studies involving grid searches across diverse configurations, we discover universal scaling laws governing these hyperparameters: optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. Our analysis reveals a convex optimization landscape for hyperparameters under fixed models and data size conditions. This convexity implies an optimal hyperparameter plateau. We contribute a universal, plug-and-play optimal hyperparameter tool for the community. Its estimated values on the test set are merely 0.07\% away from the globally optimal LLM performance found via an exhaustive search. These laws demonstrate remarkable robustness across variations in model sparsity, training data distribution, and model shape. To our best known, this is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data distributions. This exhaustive optimization process demands substantial computational resources, utilizing nearly one million NVIDIA H800 GPU hours to train 3,700 LLMs of varying sizes and hyperparameters from scratch and consuming approximately 100 trillion tokens in total. To facilitate reproducibility and further research, we will progressively release all loss measurements and model checkpoints through our designated repository https://step-law.github.io/

This paper studies using foundational large language models (LLMs) to make decisions during hyperparameter optimization (HPO). Empirical evaluations demonstrate that in settings with constrained search budgets, LLMs can perform comparably or better than traditional HPO methods like random search and Bayesian optimization on standard benchmarks. Furthermore, we propose to treat the code specifying our model as a hyperparameter, which the LLM outputs, going beyond the capabilities of existing HPO approaches. Our findings suggest that LLMs are a promising tool for improving efficiency in the traditional decision-making problem of hyperparameter optimization.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm -- using only the number of iterations as feedback -- can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

We develop an end-to-end workflow for the training and implementation of co-designed neural networks (NNs) for efficient field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) hardware. Our approach leverages Hessian-aware quantization (HAWQ) of NNs, the Quantized Open Neural Network Exchange (QONNX) intermediate representation, and the hls4ml tool flow for transpiling NNs into FPGA and ASIC firmware. This makes efficient NN implementations in hardware accessible to nonexperts, in a single open-sourced workflow that can be deployed for real-time machine learning applications in a wide range of scientific and industrial settings. We demonstrate the workflow in a particle physics application involving trigger decisions that must operate at the 40 MHz collision rate of the CERN Large Hadron Collider (LHC). Given the high collision rate, all data processing must be implemented on custom ASIC and FPGA hardware within a strict area and latency. Based on these constraints, we implement an optimized mixed-precision NN classifier for high-momentum particle jets in simulated LHC proton-proton collisions.

Recent advances in deep learning methods such as LLMs and Diffusion models have created a need for improved quantization methods that can meet the computational demands of these modern architectures while maintaining accuracy. Towards this goal, we study the advantages of FP8 data formats for post-training quantization across 75 unique network architectures covering a wide range of tasks, including machine translation, language modeling, text generation, image classification, generation, and segmentation. We examine three different FP8 representations (E5M2, E4M3, and E3M4) to study the effects of varying degrees of trade-off between dynamic range and precision on model accuracy. Based on our extensive study, we developed a quantization workflow that generalizes across different network architectures. Our empirical results show that FP8 formats outperform INT8 in multiple aspects, including workload coverage (92.64% vs. 65.87%), model accuracy and suitability for a broader range of operations. Furthermore, our findings suggest that E4M3 is better suited for NLP models, whereas E3M4 performs marginally better than E4M3 on computer vision tasks. The code is publicly available on Intel Neural Compressor: https://github.com/intel/neural-compressor.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

Fine-tuning is often necessary to enhance the adaptability of Large Language Models (LLM) to downstream tasks. Nonetheless, the process of updating billions of parameters demands significant computational resources and training time, which poses a substantial obstacle to the widespread application of large-scale models in various scenarios. To address this issue, Parameter-Efficient Fine-Tuning (PEFT) has emerged as a prominent paradigm in recent research. However, current PEFT approaches that employ a limited set of global parameters (such as LoRA, which adds low-rank approximation matrices to all weights) face challenges in flexibly combining different computational modules in downstream tasks. In this work, we introduce a novel PEFT method: MoELoRA. We consider LoRA as Mixture of Experts (MoE), and to mitigate the random routing phenomenon observed in MoE, we propose the utilization of contrastive learning to encourage experts to learn distinct features. We conducted experiments on 11 tasks in math reasoning and common-sense reasoning benchmarks. With the same number of parameters, our approach outperforms LoRA significantly. In math reasoning, MoELoRA achieved an average performance that was 4.2% higher than LoRA, and demonstrated competitive performance compared to the 175B GPT-3.5 on several benchmarks.

We combine the capacity of sparsely gated Mixture-of-Experts (MoE) with the speed and stability of linear, mixing transformations to design the Sparse Mixer encoder model. Sparse Mixer slightly outperforms (<1%) BERT on GLUE and SuperGLUE, but more importantly trains 65% faster and runs inference 61% faster. We also present a faster variant, prosaically named Fast Sparse Mixer, that marginally underperforms BERT on SuperGLUE, but trains and runs nearly twice as fast. We justify the design of these two models by carefully ablating through various mixing mechanisms, MoE configurations and hyperparameters. Sparse Mixer overcomes many of the latency and stability concerns of MoE models and offers the prospect of serving sparse student models, without resorting to distilling them to dense variants.

Key-Value (KV) Caching has become an essential technique for accelerating the inference speed and throughput of generative Large Language Models~(LLMs). However, the memory footprint of the KV cache poses a critical bottleneck in LLM deployment as the cache size grows with batch size and sequence length, often surpassing even the size of the model itself. Although recent methods were proposed to select and evict unimportant KV pairs from the cache to reduce memory consumption, the potential ramifications of eviction on the generative process are yet to be thoroughly examined. In this paper, we examine the detrimental impact of cache eviction and observe that unforeseen risks arise as the information contained in the KV pairs is exhaustively discarded, resulting in safety breaches, hallucinations, and context loss. Surprisingly, we find that preserving even a small amount of information contained in the evicted KV pairs via reduced precision quantization substantially recovers the incurred degradation. On the other hand, we observe that the important KV pairs must be kept at a relatively higher precision to safeguard the generation quality. Motivated by these observations, we propose Mixed-precision KV cache~(MiKV), a reliable cache compression method that simultaneously preserves the context details by retaining the evicted KV pairs in low-precision and ensure generation quality by keeping the important KV pairs in high-precision. Experiments on diverse benchmarks and LLM backbones show that our proposed method offers a state-of-the-art trade-off between compression ratio and performance, compared to other baselines.

Model selection/optimization in conformal inference is challenging, since it may break the exchangeability between labeled and unlabeled data. We study this problem in the context of conformal selection, which uses conformal p-values to select ``interesting'' instances with large unobserved labels from a pool of unlabeled data, while controlling the FDR in finite sample. For validity, existing solutions require the model choice to be independent of the data used to construct the p-values and calibrate the selection set. However, when presented with many model choices and limited labeled data, it is desirable to (i) select the best model in a data-driven manner, and (ii) mitigate power loss due to sample splitting. This paper presents OptCS, a general framework that allows valid statistical testing (selection) after flexible data-driven model optimization. We introduce general conditions under which OptCS constructs valid conformal p-values despite substantial data reuse and handles complex p-value dependencies to maintain finite-sample FDR control via a novel multiple testing procedure. We instantiate this general recipe to propose three FDR-controlling procedures, each optimizing the models differently: (i) selecting the most powerful one among multiple pre-trained candidate models, (ii) using all data for model fitting without sample splitting, and (iii) combining full-sample model fitting and selection. We demonstrate the efficacy of our methods via simulation studies and real applications in drug discovery and alignment of large language models in radiology report generation.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

The reproducibility and transparency of large language models are crucial for advancing open research, ensuring the trustworthiness of results, and enabling investigations into data and model biases, as well as potential risks. To this end, we release OpenELM, a state-of-the-art open language model. OpenELM uses a layer-wise scaling strategy to efficiently allocate parameters within each layer of the transformer model, leading to enhanced accuracy. For example, with a parameter budget of approximately one billion parameters, OpenELM exhibits a 2.36% improvement in accuracy compared to OLMo while requiring 2times fewer pre-training tokens. Diverging from prior practices that only provide model weights and inference code, and pre-train on private datasets, our release includes the complete framework for training and evaluation of the language model on publicly available datasets, including training logs, multiple checkpoints, and pre-training configurations. We also release code to convert models to MLX library for inference and fine-tuning on Apple devices. This comprehensive release aims to empower and strengthen the open research community, paving the way for future open research endeavors. Our source code along with pre-trained model weights and training recipes is available at https://github.com/apple/corenet. Additionally, \model models can be found on HuggingFace at: https://huggingface.co/apple/OpenELM.

Approximate inference in Gaussian process (GP) models with non-conjugate likelihoods gets entangled with the learning of the model hyperparameters. We improve hyperparameter learning in GP models and focus on the interplay between variational inference (VI) and the learning target. While VI's lower bound to the marginal likelihood is a suitable objective for inferring the approximate posterior, we show that a direct approximation of the marginal likelihood as in Expectation Propagation (EP) is a better learning objective for hyperparameter optimization. We design a hybrid training procedure to bring the best of both worlds: it leverages conjugate-computation VI for inference and uses an EP-like marginal likelihood approximation for hyperparameter learning. We compare VI, EP, Laplace approximation, and our proposed training procedure and empirically demonstrate the effectiveness of our proposal across a wide range of data sets.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.

This paper focuses on the construction of a general parametric model that can be implemented executing multiple swap tests over few qubits and applying a suitable measurement protocol. The model turns out to be equivalent to a two-layer feedforward neural network which can be realized combining small quantum modules. The advantages and the perspectives of the proposed quantum method are discussed.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

The Mixture-of-Experts (MoE) paradigm has emerged as a powerful approach for scaling transformers with improved resource utilization. However, efficiently fine-tuning MoE models remains largely underexplored. Inspired by recent works on Parameter-Efficient Fine-Tuning (PEFT), we present a unified framework for integrating PEFT modules directly into the MoE mechanism. Aligning with the core principles and architecture of MoE, our framework encompasses a set of design dimensions including various functional and composition strategies. By combining design choices within our framework, we introduce Parameter-Efficient Routed Fine-Tuning (PERFT) as a flexible and scalable family of PEFT strategies tailored for MoE models. Extensive experiments on adapting OLMoE-1B-7B and Mixtral-8times7B for commonsense and arithmetic reasoning tasks demonstrate the effectiveness, scalability, and intriguing dynamics of PERFT. Additionally, we provide empirical findings for each specific design choice to facilitate better application of MoE and PEFT.

Deep neural networks have shown promise for music audio signal processing applications, often surpassing prior approaches, particularly as end-to-end models in the waveform domain. Yet results to date have tended to be constrained by low sample rates, noise, narrow domains of signal types, and/or lack of parameterized controls (i.e. "knobs"), making their suitability for professional audio engineering workflows still lacking. This work expands on prior research published on modeling nonlinear time-dependent signal processing effects associated with music production by means of a deep neural network, one which includes the ability to emulate the parameterized settings you would see on an analog piece of equipment, with the goal of eventually producing commercially viable, high quality audio, i.e. 44.1 kHz sampling rate at 16-bit resolution. The results in this paper highlight progress in modeling these effects through architecture and optimization changes, towards increasing computational efficiency, lowering signal-to-noise ratio, and extending to a larger variety of nonlinear audio effects. Toward these ends, the strategies employed involved a three-pronged approach: model speed, model accuracy, and model generalizability. Most of the presented methods provide marginal or no increase in output accuracy over the original model, with the exception of dataset manipulation. We found that limiting the audio content of the dataset, for example using datasets of just a single instrument, provided a significant improvement in model accuracy over models trained on more general datasets.

With the proliferation of domain-specific models, model merging has emerged as a set of techniques that combine the capabilities of multiple models into one that can multitask without the cost of additional training. In this paper, we propose a new model merging technique, Drop and rEscaLe via sampLing with mAgnitude (DELLA-Merging), that employs a novel pruning technique, MAGPRUNE, which shows significant advantages over DARE and TIES. MAGPRUNE first ranks the parameters in order of their magnitude and assigns higher dropout probabilities (p) to parameters with lower ranks corresponding to lower magnitudes. To approximate the original embeddings, MAGPRUNE employs a rescaling operation on the parameters that survive the random dropping by 1/(1 - p). On three different expert models considered for merging (LM, Math, Code) and corresponding benchmark datasets (AlpacaEval, GSM8K, MBPP), DELLA shows an average improvement of 2.4 points over baseline methods employing delta parameter pruning (an improvement of 3.6 points over TIES, 1.2 points over DARE), and 11.1 points over the no-pruning baseline (TA). We release the source code at: https://github.com/declare-lab/della.

Large language models (LLMs) show great performance in various tasks, but face deployment challenges from limited memory capacity and bandwidth. Low-bit weight quantization can save memory and accelerate inference. Although floating-point (FP) formats show good performance in LLM quantization, they tend to perform poorly with small group sizes or sub-4 bits. We find the reason is that the absence of asymmetry in previous FP quantization makes it unsuitable for handling asymmetric value distribution of LLM weight tensors. In this work, we propose asymmetric FP quantization (AFPQ), which sets separate scales for positive and negative values. Our method leads to large accuracy improvements and can be easily plugged into other quantization methods, including GPTQ and AWQ, for better performance. Besides, no additional storage is needed compared with asymmetric integer (INT) quantization. The code is available at https://github.com/zhangsichengsjtu/AFPQ.

This paper introduces long-context Granite code models that support effective context windows of up to 128K tokens. Our solution for scaling context length of Granite 3B/8B code models from 2K/4K to 128K consists of a light-weight continual pretraining by gradually increasing its RoPE base frequency with repository-level file packing and length-upsampled long-context data. Additionally, we also release instruction-tuned models with long-context support which are derived by further finetuning the long context base models on a mix of permissively licensed short and long-context instruction-response pairs. While comparing to the original short-context Granite code models, our long-context models achieve significant improvements on long-context tasks without any noticeable performance degradation on regular code completion benchmarks (e.g., HumanEval). We release all our long-context Granite code models under an Apache 2.0 license for both research and commercial use.

Software engineers mainly write code by editing existing programs. In contrast, large language models (LLMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of open-sourced edit data. While high-quality instruction data for code synthesis is already scarce, high-quality edit data is even scarcer. To fill this gap, we develop a synthetic data generation algorithm called LintSeq. This algorithm refactors existing code into a sequence of code edits by using a linter to procedurally sample across the error-free insertions that can be used to sequentially write programs. It outputs edit sequences as text strings consisting of consecutive program diffs. To test LintSeq, we use it to refactor a dataset of instruction + program pairs into instruction + program-diff-sequence tuples. Then, we instruction finetune a series of smaller LLMs ranging from 2.6B to 14B parameters on both the re-factored and original versions of this dataset, comparing zero-shot performance on code synthesis benchmarks. We show that during repeated sampling, edit sequence finetuned models produce more diverse programs than baselines. This results in better inference-time scaling for benchmark coverage as a function of samples, i.e. the fraction of problems "pass@k" solved by any attempt given "k" tries. For example, on HumanEval pass@50, small LLMs finetuned on synthetic edit sequences are competitive with GPT-4 and outperform models finetuned on the baseline dataset by +20% (+/-3%) in absolute score. Finally, we also pretrain our own tiny LMs for code understanding. We show that finetuning tiny models on synthetic code edits results in state-of-the-art code synthesis for the on-device model class. Our 150M parameter edit sequence LM matches or outperforms code models with twice as many parameters, both with and without repeated sampling, including Codex and AlphaCode.

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We apply the inverse Fourier transform to obtain the covariance function (by Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. Next, we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to promote computational efficiency and scalability, without low-rank approximations. We show the advantage of our method in systematic experiments. The code is released at https://github.com/xuangu-fang/Gaussian-Process-Slover-for-High-Freq-PDE.

The extrapolation capability of Large Language Models (LLMs) based on Rotary Position Embedding is currently a topic of considerable interest. The mainstream approach to addressing extrapolation with LLMs involves modifying RoPE by replacing 10000, the rotary base of theta_n={10000}^{-2n/d} in the original RoPE, with a larger value and providing longer fine-tuning text. In this work, we first observe that fine-tuning a RoPE-based LLM with either a smaller or larger base in pre-training context length could significantly enhance its extrapolation performance. After that, we propose \textit{Scaling Laws of RoPE-based Extrapolation}, a unified framework from the periodic perspective, to describe the relationship between the extrapolation performance and base value as well as tuning context length. In this process, we also explain the origin of the RoPE-based extrapolation issue by \textit{critical dimension for extrapolation}. Besides these observations and analyses, we achieve extrapolation up to 1 million context length within only 16K training length on LLaMA2 7B and 13B.

The demand for inference on extremely large scale LLMs has seen enormous growth in the recent months. It made evident the colossal shortage of dedicated hardware capable of efficient and fast processing of the involved compute and memory movement. The problem is aggravated by the exploding raise in the lengths of the sequences being processed, since those require efficient on-chip storage of the KV-cache of size proportional to the sequence length. To make the required compute feasible and fit the involved data into available memory, numerous quantization techniques have been proposed that allow accurate quantization for both weights and activations. One of the main recent breakthroughs in this direction was introduction of the family of Block Floating Point (BFP) formats characterized by a block of mantissas with a shared scale factor. These enable memory- power-, and compute- efficient hardware support of the tensor operations and provide extremely good quantization accuracy. The main issues preventing widespread application of block formats is caused by the presence of outliers in weights and activations since those affect the accuracy of the other values in the same block. In this paper, we focus on the most critical problem of limited KV-cache storage. We propose a novel approach enabling usage of low precision BFP formats without compromising the resulting model accuracy. We exploit the common channel-wise patterns exhibited by the outliers to rearrange them in such a way, that their quantization quality is significantly improved. The methodology yields 2x savings in the memory footprint without significant degradation of the model's accuracy. Importantly, the rearrangement of channels happens at the compile time and thus has no impact on the inference latency.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

This paper presents NT-Java-1.1B, an open-source specialized code language model built on StarCoderBase-1.1B, designed for coding tasks in Java programming. NT-Java-1.1B achieves state-of-the-art performance, surpassing its base model and majority of other models of similar size on MultiPL-E Java code benchmark. While there have been studies on extending large, generic pre-trained models to improve proficiency in specific programming languages like Python, similar investigations on small code models for other programming languages are lacking. Large code models require specialized hardware like GPUs for inference, highlighting the need for research into building small code models that can be deployed on developer desktops. This paper addresses this research gap by focusing on the development of a small Java code model, NT-Java-1.1B, and its quantized versions, which performs comparably to open models around 1.1B on MultiPL-E Java code benchmarks, making them ideal for desktop deployment. This paper establishes the foundation for specialized models across languages and sizes for a family of NT Models.

The burgeoning computational demands for training large language models (LLMs) necessitate efficient methods, including quantized training, which leverages low-bit arithmetic operations to reduce costs. While FP8 precision has shown potential, leveraging FP4 remains challenging due to inherent quantization errors and limited representation capability. Based on the Transformer architecture, we present an FP4 training scheme for LLMs, overcoming these obstacles through mixed-precision quantization strategies tailed for different modules and training stages. This allows us to apply the precision level suitable to distinct components within the model, ensuring that multi-head attention and linear layers are handled appropriately. Our pretraining recipe ensures stability in backpropagation by incorporating fine-grained quantization methods with a target precision training schedule. Experimental results demonstrate that our FP4 training scheme achieves accuracy comparable to BF16 and FP8, with smaller theoretical computational cost. With the advent of next-generation hardware supporting FP4, our method sets the foundation for efficient ultra-low precision training.

We present a new approach to constructing and fitting dipoles and higher-order multipoles in synthetic galaxy samples over the sky. Within our Bayesian paradigm, we illustrate that this technique is robust to masked skies, allowing us to make credible inferences about the relative contributions of each multipole. We also show that dipoles can be recovered in surveys with small footprints, determining the requisite source counts required for concrete estimation of the dipole parameters. This work is motivated by recent probes of the cosmic dipole in galaxy catalogues. Namely, the kinematic dipole of the Cosmic Microwave Background, as arising from the motion of our heliocentric frame at approx 370 km,s^{-1}, implies that an analogous dipole should be observed in the number counts of galaxies in flux-density-limited samples. Recent studies have reported a dipole aligning with the kinematic dipole but with an anomalously large amplitude. Accordingly, our new technique will be important as forthcoming galaxy surveys are made available and for revisiting previous data.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

With the increasingly powerful performances and enormous scales of Pretrained Language Models (PLMs), promoting parameter efficiency in fine-tuning has become a crucial need for effective and efficient adaptation to various downstream tasks. One representative line of fine-tuning methods is Orthogonal Fine-tuning (OFT), which rigorously preserves the angular distances within the parameter space to preserve the pretrained knowledge. Despite the empirical effectiveness, OFT still suffers low parameter efficiency at O(d^2) and limited capability of downstream adaptation. Inspired by Givens rotation, in this paper, we proposed quasi-Givens Orthogonal Fine-Tuning (qGOFT) to address the problems. We first use O(d) Givens rotations to accomplish arbitrary orthogonal transformation in SO(d) with provable equivalence, reducing parameter complexity from O(d^2) to O(d). Then we introduce flexible norm and relative angular adjustments under soft orthogonality regularization to enhance the adaptation capability of downstream semantic deviations. Extensive experiments on various tasks and PLMs validate the effectiveness of our methods.

Hampering the interpretation of benchmark scores, evaluation data contamination has become a growing concern in the evaluation of LLMs, and an active area of research studies its effects. While evaluation data contamination is easily understood intuitively, it is surprisingly difficult to define precisely which samples should be considered contaminated and, consequently, how it impacts benchmark scores. We propose that these questions should be addressed together and that contamination metrics can be assessed based on whether models benefit from the examples they mark contaminated. We propose a novel analysis method called ConTAM, and show with a large scale survey of existing and novel n-gram based contamination metrics across 13 benchmarks and 7 models from 2 different families that ConTAM can be used to better understand evaluation data contamination and its effects. We find that contamination may have a much larger effect than reported in recent LLM releases and benefits models differently at different scales. We also find that considering only the longest contaminated substring provides a better signal than considering a union of all contaminated substrings, and that doing model and benchmark specific threshold analysis greatly increases the specificity of the results. Lastly, we investigate the impact of hyperparameter choices, finding that, among other things, both using larger values of n and disregarding matches that are infrequent in the pre-training data lead to many false negatives. With ConTAM, we provide a method to empirically ground evaluation data contamination metrics in downstream effects. With our exploration, we shed light on how evaluation data contamination can impact LLMs and provide insight into the considerations important when doing contamination analysis. We end our paper by discussing these in more detail and providing concrete suggestions for future work.

We introduce StableLM 2 1.6B, the first in a new generation of our language model series. In this technical report, we present in detail the data and training procedure leading to the base and instruction-tuned versions of StableLM 2 1.6B. The weights for both models are available via Hugging Face for anyone to download and use. The report contains thorough evaluations of these models, including zero- and few-shot benchmarks, multilingual benchmarks, and the MT benchmark focusing on multi-turn dialogues. At the time of publishing this report, StableLM 2 1.6B was the state-of-the-art open model under 2B parameters by a significant margin. Given its appealing small size, we also provide throughput measurements on a number of edge devices. In addition, we open source several quantized checkpoints and provide their performance metrics compared to the original model.

Averaging the parameters of models that have the same architecture and initialization can provide a means of combining their respective capabilities. In this paper, we take the perspective that this "merging" operation can be seen as choosing parameters that approximately maximize the joint likelihood of the posteriors of the models' parameters. Computing a simple average of the models' parameters therefore corresponds to making an isotropic Gaussian approximation to their posteriors. We develop an alternative merging procedure based on the Laplace approximation where we approximate each model's posterior as a Gaussian distribution whose precision matrix corresponds to its Fisher information. We first show that our "Fisher merging" technique provides a performance boost in settings where simple parameter averaging is currently used -- specifically, robust fine-tuning and model ensembling. Then, we compare merging to standard gradient-based transfer learning and demonstrate that merging enables a fundamentally different method for transferring capabilities across models. Specifically, we show that Fisher merging is competitive with gradient-based transfer learning approaches (while being significantly cheaper) in intermediate-task training and domain-adaptive pre-training. We also show that our merging procedure makes it possible to combine models in previously unexplored ways. We release our code to facilitate future research into methods for merging models.

Instruction Tuning involves finetuning a language model on a collection of instruction-formatted datasets in order to enhance the generalizability of the model to unseen tasks. Studies have shown the importance of balancing different task proportions during finetuning, but finding the right balance remains challenging. Unfortunately, there's currently no systematic method beyond manual tuning or relying on practitioners' intuition. In this paper, we introduce SMART (Submodular data Mixture strAtegy for instRuction Tuning) - a novel data mixture strategy which makes use of a submodular function to assign importance scores to tasks which are then used to determine the mixture weights. Given a fine-tuning budget, SMART redistributes the budget among tasks and selects non-redundant samples from each task. Experimental results demonstrate that SMART significantly outperforms traditional methods such as examples proportional mixing and equal mixing. Furthermore, SMART facilitates the creation of data mixtures based on a few representative subsets of tasks alone and through task pruning analysis, we reveal that in a limited budget setting, allocating budget among a subset of representative tasks yields superior performance compared to distributing the budget among all tasks. The code for reproducing our results is open-sourced at https://github.com/kowndinya-renduchintala/SMART.