Daily Papers

Over the past few years, softmax and SGD have become a commonly used component and the default training strategy in CNN frameworks, respectively. However, when optimizing CNNs with SGD, the saturation behavior behind softmax always gives us an illusion of training well and then is omitted. In this paper, we first emphasize that the early saturation behavior of softmax will impede the exploration of SGD, which sometimes is a reason for model converging at a bad local-minima, then propose Noisy Softmax to mitigating this early saturation issue by injecting annealed noise in softmax during each iteration. This operation based on noise injection aims at postponing the early saturation and further bringing continuous gradients propagation so as to significantly encourage SGD solver to be more exploratory and help to find a better local-minima. This paper empirically verifies the superiority of the early softmax desaturation, and our method indeed improves the generalization ability of CNN model by regularization. We experimentally find that this early desaturation helps optimization in many tasks, yielding state-of-the-art or competitive results on several popular benchmark datasets.

Differentiable architecture search (DARTS) yields highly efficient gradient-based neural architecture search (NAS) by relaxing the discrete operation selection to optimize continuous architecture parameters that maps NAS from the discrete optimization to a continuous problem. DARTS then remaps the relaxed supernet back to the discrete space by one-off post-search pruning to obtain the final architecture (finalnet). Some emerging works argue that this remap is inherently prone to mismatch the network between training and evaluation which leads to performance discrepancy and even model collapse in extreme cases. We propose to close the gap between the relaxed supernet in training and the pruned finalnet in evaluation through utilizing small temperature to sparsify the continuous distribution in the training phase. To this end, we first formulate sparse-noisy softmax to get around gradient saturation. We then propose an exponential temperature schedule to better control the outbound distribution and elaborate an entropy-based adaptive scheme to finally achieve the enhancement. We conduct extensive experiments to verify the efficiency and efficacy of our method.

The Softmax function is ubiquitous in machine learning, multiple previous works suggested faster alternatives for it. In this paper we propose a way to compute classical Softmax with fewer memory accesses and hypothesize that this reduction in memory accesses should improve Softmax performance on actual hardware. The benchmarks confirm this hypothesis: Softmax accelerates by up to 1.3x and Softmax+TopK combined and fused by up to 5x.

In continual learning, many classifiers use softmax function to learn confidence. However, numerous studies have pointed out its inability to accurately determine confidence distributions for outliers, often referred to as epistemic uncertainty. This inherent limitation also curtails the accurate decisions for selecting what to forget and keep in previously trained confidence distributions over continual learning process. To address the issue, we revisit the effects of masking softmax function. While this method is both simple and prevalent in literature, its implication for retaining confidence distribution during continual learning, also known as stability, has been under-investigated. In this paper, we revisit the impact of softmax masking, and introduce a methodology to utilize its confidence preservation effects. In class- and task-incremental learning benchmarks with and without memory replay, our approach significantly increases stability while maintaining sufficiently large plasticity. In the end, our methodology shows better overall performance than state-of-the-art methods, particularly in the use with zero or small memory. This lays a simple and effective foundation of strongly stable replay-based continual learning.

Available training data for named entity recognition (NER) often contains a significant percentage of incorrect labels for entity types and entity boundaries. Such label noise poses challenges for supervised learning and may significantly deteriorate model quality. To address this, prior work proposed various noise-robust learning approaches capable of learning from data with partially incorrect labels. These approaches are typically evaluated using simulated noise where the labels in a clean dataset are automatically corrupted. However, as we show in this paper, this leads to unrealistic noise that is far easier to handle than real noise caused by human error or semi-automatic annotation. To enable the study of the impact of various types of real noise, we introduce NoiseBench, an NER benchmark consisting of clean training data corrupted with 6 types of real noise, including expert errors, crowdsourcing errors, automatic annotation errors and LLM errors. We present an analysis that shows that real noise is significantly more challenging than simulated noise, and show that current state-of-the-art models for noise-robust learning fall far short of their theoretically achievable upper bound. We release NoiseBench to the research community.

This paper explores the scenarios under which an attacker can claim that 'Noise and access to the softmax layer of the model is all you need' to steal the weights of a convolutional neural network whose architecture is already known. We were able to achieve 96% test accuracy using the stolen MNIST model and 82% accuracy using the stolen KMNIST model learned using only i.i.d. Bernoulli noise inputs. We posit that this theft-susceptibility of the weights is indicative of the complexity of the dataset and propose a new metric that captures the same. The goal of this dissemination is to not just showcase how far knowing the architecture can take you in terms of model stealing, but to also draw attention to this rather idiosyncratic weight learnability aspects of CNNs spurred by i.i.d. noise input. We also disseminate some initial results obtained with using the Ising probability distribution in lieu of the i.i.d. Bernoulli distribution.

Despite achieving state-of-the-art results in nearly all Natural Language Processing applications, fine-tuning Transformer-based language models still requires a significant amount of labeled data to work. A well known technique to reduce the amount of human effort in acquiring a labeled dataset is Active Learning (AL): an iterative process in which only the minimal amount of samples is labeled. AL strategies require access to a quantified confidence measure of the model predictions. A common choice is the softmax activation function for the final layer. As the softmax function provides misleading probabilities, this paper compares eight alternatives on seven datasets. Our almost paradoxical finding is that most of the methods are too good at identifying the true most uncertain samples (outliers), and that labeling therefore exclusively outliers results in worse performance. As a heuristic we propose to systematically ignore samples, which results in improvements of various methods compared to the softmax function.

We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classification tasks, which exploits the progress of the early learning phase. In contrast with existing approaches, which use the model output during early learning to detect the examples with clean labels, and either ignore or attempt to correct the false labels, we take a different route and instead capitalize on early learning via regularization. There are two key elements to our approach. First, we leverage semi-supervised learning techniques to produce target probabilities based on the model outputs. Second, we design a regularization term that steers the model towards these targets, implicitly preventing memorization of the false labels. The resulting framework is shown to provide robustness to noisy annotations on several standard benchmarks and real-world datasets, where it achieves results comparable to the state of the art.

A key property of reasoning systems is the ability to make sharp decisions on their input data. For contemporary AI systems, a key carrier of sharp behaviour is the softmax function, with its capability to perform differentiable query-key lookups. It is a common belief that the predictive power of networks leveraging softmax arises from "circuits" which sharply perform certain kinds of computations consistently across many diverse inputs. However, for these circuits to be robust, they would need to generalise well to arbitrary valid inputs. In this paper, we dispel this myth: even for tasks as simple as finding the maximum key, any learned circuitry must disperse as the number of items grows at test time. We attribute this to a fundamental limitation of the softmax function to robustly approximate sharp functions, prove this phenomenon theoretically, and propose adaptive temperature as an ad-hoc technique for improving the sharpness of softmax at inference time.

During both pretraining and fine-tuning, Large Language Models (LLMs) are trained on trillions of tokens of text of widely varying quality. Both phases of training typically involve heuristically filtering out ``low-quality'' or noisy training samples, yet little is known quantitatively about how the type or intensity of noise affects downstream performance. In this work, we study how noise in chain of thought (CoT) impacts task performance in the highly-controlled setting of algorithmically solvable tasks. First, we develop the Traced Integer (TInt) framework to generate highly customizable noised execution traces for any arithmetic function on lists of integers. We then define two types of noise: static noise, a local form of noise which is applied after the CoT trace is computed, and dynamic noise, a global form of noise which propagates errors in the trace as it is computed. We then evaluate the test performance of pretrained models both prompted and fine-tuned on noised datasets with varying levels of dataset contamination and intensity. We find fine-tuned models are extremely robust to high levels of static noise but struggle significantly more with lower levels of dynamic noise. In contrast, few-shot prompted models appear more sensitive to even static noise. We conclude with a discussion of how our findings impact noise filtering best-practices, in particular emphasizing the importance of removing samples containing destructive dynamic noise with global errors.

This study addresses the challenge of noise in training datasets for Direct Preference Optimization (DPO), a method for aligning Large Language Models (LLMs) with human preferences. We categorize noise into pointwise noise, which includes low-quality data points, and pairwise noise, which encompasses erroneous data pair associations that affect preference rankings. Utilizing Distributionally Robust Optimization (DRO), we enhance DPO's resilience to these types of noise. Our theoretical insights reveal that DPO inherently embeds DRO principles, conferring robustness to pointwise noise, with the regularization coefficient beta playing a critical role in its noise resistance. Extending this framework, we introduce Distributionally Robustifying DPO (Dr. DPO), which integrates pairwise robustness by optimizing against worst-case pairwise scenarios. The novel hyperparameter beta' in Dr. DPO allows for fine-tuned control over data pair reliability, providing a strategic balance between exploration and exploitation in noisy training environments. Empirical evaluations demonstrate that Dr. DPO substantially improves the quality of generated text and response accuracy in preference datasets, showcasing enhanced performance in both noisy and noise-free settings. The code is available at https://github.com/junkangwu/Dr_DPO.

We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization techniques. It requires only loose bounds on d0 and the noise magnitude, provides high probability guarantees under sub-Gaussian noise, and is also near-optimal in the non-smooth case. Our experiments show consistent, strong performance on convex problems and mixed results on neural network training.

Retrieval-Augmented Generation (RAG) has emerged as a crucial method for addressing hallucinations in large language models (LLMs). While recent research has extended RAG models to complex noisy scenarios, these explorations often confine themselves to limited noise types and presuppose that noise is inherently detrimental to LLMs, potentially deviating from real-world retrieval environments and restricting practical applicability. In this paper, we define seven distinct noise types from a linguistic perspective and establish a Noise RAG Benchmark (NoiserBench), a comprehensive evaluation framework encompassing multiple datasets and reasoning tasks. Through empirical evaluation of eight representative LLMs with diverse architectures and scales, we reveal that these noises can be further categorized into two practical groups: noise that is beneficial to LLMs (aka beneficial noise) and noise that is harmful to LLMs (aka harmful noise). While harmful noise generally impairs performance, beneficial noise may enhance several aspects of model capabilities and overall performance. Our analysis offers insights for developing more robust, adaptable RAG solutions and mitigating hallucinations across diverse retrieval scenarios.

Supervised fine-tuning (SFT) plays a crucial role in adapting large language models (LLMs) to specific domains or tasks. However, as demonstrated by empirical experiments, the collected data inevitably contains noise in practical applications, which poses significant challenges to model performance on downstream tasks. Therefore, there is an urgent need for a noise-robust SFT framework to enhance model capabilities in downstream tasks. To address this challenge, we introduce a robust SFT framework (RobustFT) that performs noise detection and relabeling on downstream task data. For noise identification, our approach employs a multi-expert collaborative system with inference-enhanced models to achieve superior noise detection. In the denoising phase, we utilize a context-enhanced strategy, which incorporates the most relevant and confident knowledge followed by careful assessment to generate reliable annotations. Additionally, we introduce an effective data selection mechanism based on response entropy, ensuring only high-quality samples are retained for fine-tuning. Extensive experiments conducted on multiple LLMs across five datasets demonstrate RobustFT's exceptional performance in noisy scenarios.

Detecting test samples drawn sufficiently far away from the training distribution statistically or adversarially is a fundamental requirement for deploying a good classifier in many real-world machine learning applications. However, deep neural networks with the softmax classifier are known to produce highly overconfident posterior distributions even for such abnormal samples. In this paper, we propose a simple yet effective method for detecting any abnormal samples, which is applicable to any pre-trained softmax neural classifier. We obtain the class conditional Gaussian distributions with respect to (low- and upper-level) features of the deep models under Gaussian discriminant analysis, which result in a confidence score based on the Mahalanobis distance. While most prior methods have been evaluated for detecting either out-of-distribution or adversarial samples, but not both, the proposed method achieves the state-of-the-art performances for both cases in our experiments. Moreover, we found that our proposed method is more robust in harsh cases, e.g., when the training dataset has noisy labels or small number of samples. Finally, we show that the proposed method enjoys broader usage by applying it to class-incremental learning: whenever out-of-distribution samples are detected, our classification rule can incorporate new classes well without further training deep models.

Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these noisy labels is noise modelling where the underlying noise process is modelled. In this work, we study the quality of these estimated noise models from the theoretical side by deriving the expected error of the noise model. Apart from evaluating the theoretical results on commonly used synthetic noise, we also publish NoisyNER, a new noisy label dataset from the NLP domain that was obtained through a realistic distant supervision technique. It provides seven sets of labels with differing noise patterns to evaluate different noise levels on the same instances. Parallel, clean labels are available making it possible to study scenarios where a small amount of gold-standard data can be leveraged. Our theoretical results and the corresponding experiments give insights into the factors that influence the noise model estimation like the noise distribution and the sampling technique.

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.

Despite being the standard loss function to train multi-class neural networks, the log-softmax has two potential limitations. First, it involves computations that scale linearly with the number of output classes, which can restrict the size of problems we are able to tackle with current hardware. Second, it remains unclear how close it matches the task loss such as the top-k error rate or other non-differentiable evaluation metrics which we aim to optimize ultimately. In this paper, we introduce an alternative classification loss function, the Z-loss, which is designed to address these two issues. Unlike the log-softmax, it has the desirable property of belonging to the spherical loss family (Vincent et al., 2015), a class of loss functions for which training can be performed very efficiently with a complexity independent of the number of output classes. We show experimentally that it significantly outperforms the other spherical loss functions previously investigated. Furthermore, we show on a word language modeling task that it also outperforms the log-softmax with respect to certain ranking scores, such as top-k scores, suggesting that the Z-loss has the flexibility to better match the task loss. These qualities thus makes the Z-loss an appealing candidate to train very efficiently large output networks such as word-language models or other extreme classification problems. On the One Billion Word (Chelba et al., 2014) dataset, we are able to train a model with the Z-loss 40 times faster than the log-softmax and more than 4 times faster than the hierarchical softmax.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the appearance of robust associative memories. We first propose a simplified model of noise in the brain, taking into account synaptic noise and interference from neurons external to the network. When coarsely quantized, we show that this noise can be reduced to insertions and erasures. We take a neural network with recurrent modifiable connections, and subject it to noisy external inputs. We introduce an energy usage limitation principle in the network as well as consolidated Hebbian learning, resulting in an incremental processing of inputs. We show that the connections naturally formed correspond to state-of-the-art binary sparse associative memories.

Post-training quantization (PTQ) is the go-to compression technique for large generative models, such as stable diffusion or large language models. PTQ methods commonly keep the softmax activation in higher precision as it has been shown to be very sensitive to quantization noise. However, this can lead to a significant runtime and power overhead during inference on resource-constraint edge devices. In this work, we investigate the source of the softmax sensitivity to quantization and show that the quantization operation leads to a large bias in the softmax output, causing accuracy degradation. To overcome this issue, we propose an offline bias correction technique that improves the quantizability of softmax without additional compute during deployment, as it can be readily absorbed into the quantization parameters. We demonstrate the effectiveness of our method on stable diffusion v1.5 and 125M-size OPT language model, achieving significant accuracy improvement for 8-bit quantized softmax.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

Robust loss functions are essential for training accurate deep neural networks (DNNs) in the presence of noisy (incorrect) labels. It has been shown that the commonly used Cross Entropy (CE) loss is not robust to noisy labels. Whilst new loss functions have been designed, they are only partially robust. In this paper, we theoretically show by applying a simple normalization that: any loss can be made robust to noisy labels. However, in practice, simply being robust is not sufficient for a loss function to train accurate DNNs. By investigating several robust loss functions, we find that they suffer from a problem of underfitting. To address this, we propose a framework to build robust loss functions called Active Passive Loss (APL). APL combines two robust loss functions that mutually boost each other. Experiments on benchmark datasets demonstrate that the family of new loss functions created by our APL framework can consistently outperform state-of-the-art methods by large margins, especially under large noise rates such as 60% or 80% incorrect labels.

SGD does not produce robust results on datasets with label noise. Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction. In this paper, as an alternative to SGD, we recommend using samples with loss less than a threshold value determined during the optimization process, instead of using all samples in the mini-batch. Our proposed method, Adaptive-k, aims to exclude label noise samples from the optimization process and make the process robust. On noisy datasets, we found that using a threshold-based approach, such as Adaptive-k, produces better results than using all samples or a fixed number of low-loss samples in the mini-batch. Based on our theoretical analysis and experimental results, we show that the Adaptive-k method is closest to the performance of the oracle, in which noisy samples are entirely removed from the dataset. Adaptive-k is a simple but effective method. It does not require prior knowledge of the noise ratio of the dataset, does not require additional model training, and does not increase training time significantly. The code for Adaptive-k is available at https://github.com/enesdedeoglu-TR/Adaptive-k

Diffusion models learn to restore noisy data, which is corrupted with different levels of noise, by optimizing the weighted sum of the corresponding loss terms, i.e., denoising score matching loss. In this paper, we show that restoring data corrupted with certain noise levels offers a proper pretext task for the model to learn rich visual concepts. We propose to prioritize such noise levels over other levels during training, by redesigning the weighting scheme of the objective function. We show that our simple redesign of the weighting scheme significantly improves the performance of diffusion models regardless of the datasets, architectures, and sampling strategies.

Noisy partial label learning (noisy PLL) is an important branch of weakly supervised learning. Unlike PLL where the ground-truth label must conceal in the candidate label set, noisy PLL relaxes this constraint and allows the ground-truth label may not be in the candidate label set. To address this challenging problem, most of the existing works attempt to detect noisy samples and estimate the ground-truth label for each noisy sample. However, detection errors are unavoidable. These errors can accumulate during training and continuously affect model optimization. To this end, we propose a novel framework for noisy PLL with theoretical guarantees, called ``Adjusting Label Importance Mechanism (ALIM)''. It aims to reduce the negative impact of detection errors by trading off the initial candidate set and model outputs. ALIM is a plug-in strategy that can be integrated with existing PLL approaches. Experimental results on benchmark datasets demonstrate that our method can achieve state-of-the-art performance on noisy PLL. \textcolor[rgb]{0.93,0.0,0.47}{Our code can be found in Supplementary Material}.

Existing speculative decoding methods typically require additional model structure and training processes to assist the model for draft token generation. This makes the migration of acceleration methods to the new model more costly and more demanding on device memory. To address this problem, we propose the Make Some Noise (MSN) training framework as a replacement for the supervised fine-tuning stage of the large language model. The training method simply introduces some noise at the input for the model to learn the denoising task. It significantly enhances the parallel decoding capability of the model without affecting the original task capability. In addition, we propose a tree-based retrieval-augmented Jacobi (TR-Jacobi) decoding strategy to further improve the inference speed of MSN models. Experiments in both the general and code domains have shown that MSN can improve inference speed by 2.3-2.7x times without compromising model performance. The MSN model also achieves comparable acceleration ratios to the SOTA model with additional model structure on Spec-Bench.

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons behind the delayed generalization and its dependence on regularization remain unclear. In this work, we argue that without regularization, grokking tasks push models to the edge of numerical stability, introducing floating point errors in the Softmax function, which we refer to as Softmax Collapse (SC). We demonstrate that SC prevents grokking and that mitigating SC enables grokking without regularization. Investigating the root cause of SC, we find that beyond the point of overfitting, the gradients strongly align with what we call the na\"ive loss minimization (NLM) direction. This component of the gradient does not alter the model's predictions but decreases the loss by scaling the logits, typically by scaling the weights along their current direction. We show that this scaling of the logits explains the delay in generalization characteristic of grokking and eventually leads to SC, halting further learning. To validate our hypotheses, we introduce two key contributions that address the challenges in grokking tasks: StableMax, a new activation function that prevents SC and enables grokking without regularization, and perpGrad, a training algorithm that promotes quick generalization in grokking tasks by preventing NLM altogether. These contributions provide new insights into grokking, elucidating its delayed generalization, reliance on regularization, and the effectiveness of existing grokking-inducing methods. Code for this paper is available at https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability.

Inducing and leveraging sparse activations during training and inference is a promising avenue for improving the computational efficiency of deep networks, which is increasingly important as network sizes continue to grow and their application becomes more widespread. Here we use the large width Gaussian process limit to analyze the behaviour, at random initialization, of nonlinear activations that induce sparsity in the hidden outputs. A previously unreported form of training instability is proven for arguably two of the most natural candidates for hidden layer sparsification; those being a shifted ReLU (phi(x)=max(0, x-tau) for tauge 0) and soft thresholding (phi(x)=0 for |x|letau and x-sign(x)tau for |x|>tau). We show that this instability is overcome by clipping the nonlinear activation magnitude, at a level prescribed by the shape of the associated Gaussian process variance map. Numerical experiments verify the theory and show that the proposed magnitude clipped sparsifying activations can be trained with training and test fractional sparsity as high as 85\% while retaining close to full accuracy.

Major advancements have been made in the field of object detection and segmentation recently. However, when it comes to rare categories, the state-of-the-art methods fail to detect them, resulting in a significant performance gap between rare and frequent categories. In this paper, we identify that Sigmoid or Softmax functions used in deep detectors are a major reason for low performance and are sub-optimal for long-tailed detection and segmentation. To address this, we develop a Gumbel Optimized Loss (GOL), for long-tailed detection and segmentation. It aligns with the Gumbel distribution of rare classes in imbalanced datasets, considering the fact that most classes in long-tailed detection have low expected probability. The proposed GOL significantly outperforms the best state-of-the-art method by 1.1% on AP , and boosts the overall segmentation by 9.0% and detection by 8.0%, particularly improving detection of rare classes by 20.3%, compared to Mask-RCNN, on LVIS dataset. Code available at: https://github.com/kostas1515/GOL

Real-world analog systems intrinsically suffer from noise that can impede model convergence and accuracy on a variety of deep learning models. We demonstrate that differentiable activations like GELU and SiLU enable robust propagation of gradients which help to mitigate analog quantization error that is ubiquitous to all analog systems. We perform analysis and training of convolutional, linear, and transformer networks in the presence of quantized noise. Here, we are able to demonstrate that continuously differentiable activation functions are significantly more noise resilient over conventional rectified activations. As in the case of ReLU, the error in gradients are 100x higher than those in GELU near zero. Our findings provide guidance for selecting appropriate activations to realize performant and reliable hardware implementations across several machine learning domains such as computer vision, signal processing, and beyond.

While prior research has proposed a plethora of methods that build neural classifiers robust against adversarial robustness, practitioners are still reluctant to adopt them due to their unacceptably severe clean accuracy penalties. This paper significantly alleviates this accuracy-robustness trade-off by mixing the output probabilities of a standard classifier and a robust classifier, where the standard network is optimized for clean accuracy and is not robust in general. We show that the robust base classifier's confidence difference for correct and incorrect examples is the key to this improvement. In addition to providing intuitions and empirical evidence, we theoretically certify the robustness of the mixed classifier under realistic assumptions. Furthermore, we adapt an adversarial input detector into a mixing network that adaptively adjusts the mixture of the two base models, further reducing the accuracy penalty of achieving robustness. The proposed flexible method, termed "adaptive smoothing", can work in conjunction with existing or even future methods that improve clean accuracy, robustness, or adversary detection. Our empirical evaluation considers strong attack methods, including AutoAttack and adaptive attack. On the CIFAR-100 dataset, our method achieves an 85.21% clean accuracy while maintaining a 38.72% ell_infty-AutoAttacked (epsilon = 8/255) accuracy, becoming the second most robust method on the RobustBench CIFAR-100 benchmark as of submission, while improving the clean accuracy by ten percentage points compared with all listed models. The code that implements our method is available at https://github.com/Bai-YT/AdaptiveSmoothing.

Large language models (LLMs) have shown remarkable capabilities in code generation. However, the effects of hallucinations (e.g., output noise) make it particularly challenging for LLMs to generate high-quality code in one pass. In this work, we propose a simple and effective uncertainty-aware selective contrastive decoding (USCD) mechanism to improve the quality of one-pass code generation in LLMs and reduce the impact of output noise. To be specific, we first elaborately designed a negative prompt (namely lame prompt) to output noise by removing input-output examples from the standard few-shot prompt. Our preliminary study shows that the Jensen-Shannon divergence (JS divergence) between token distribution uncertainty and the output noise is relatively low (approximately 0.25), indicating their high relevance. Then, we selectively eliminate output noise induced by lame prompts based on the uncertainty of the prediction distribution from the standard prompt. Notably, our proposed plug-and-play mechanism is an inference-only method, enjoying appealing flexibility. Extensive experiments on widely used benchmarks, e.g., HumanEval, MBPP, and MultiPL-E, upon several LLMs (i.e., Inocder-6b, CodeLlama-7b, WizardCoder-15b, StarCoder, and Llama2-7b), demonstrate that our proposed USCD significantly improves one-pass code generation, with an average pass@1 scores increase of 16.59\%. We will release code and data on GitHub.

In today's heavily overparameterized models, the value of the training loss provides few guarantees on model generalization ability. Indeed, optimizing only the training loss value, as is commonly done, can easily lead to suboptimal model quality. Motivated by prior work connecting the geometry of the loss landscape and generalization, we introduce a novel, effective procedure for instead simultaneously minimizing loss value and loss sharpness. In particular, our procedure, Sharpness-Aware Minimization (SAM), seeks parameters that lie in neighborhoods having uniformly low loss; this formulation results in a min-max optimization problem on which gradient descent can be performed efficiently. We present empirical results showing that SAM improves model generalization across a variety of benchmark datasets (e.g., CIFAR-10, CIFAR-100, ImageNet, finetuning tasks) and models, yielding novel state-of-the-art performance for several. Additionally, we find that SAM natively provides robustness to label noise on par with that provided by state-of-the-art procedures that specifically target learning with noisy labels. We open source our code at https://github.com/google-research/sam.

The lack of clean speech is a practical challenge to the development of speech enhancement systems, which means that there is an inevitable mismatch between their training criterion and evaluation metric. In response to this unfavorable situation, we propose a training and inference strategy that additionally uses enhanced speech as a target by improving the previously proposed noisy-target training (NyTT). Because homogeneity between in-domain noise and extraneous noise is the key to the effectiveness of NyTT, we train various student models by remixing 1) the teacher model's estimated speech and noise for enhanced-target training or 2) raw noisy speech and the teacher model's estimated noise for noisy-target training. Experimental results show that our proposed method outperforms several baselines, especially with the teacher/student inference, where predicted clean speech is derived successively through the teacher and final student models.

Mixture-of-experts (MoE) model incorporates the power of multiple submodels via gating functions to achieve greater performance in numerous regression and classification applications. From a theoretical perspective, while there have been previous attempts to comprehend the behavior of that model under the regression settings through the convergence analysis of maximum likelihood estimation in the Gaussian MoE model, such analysis under the setting of a classification problem has remained missing in the literature. We close this gap by establishing the convergence rates of density estimation and parameter estimation in the softmax gating multinomial logistic MoE model. Notably, when part of the expert parameters vanish, these rates are shown to be slower than polynomial rates owing to an inherent interaction between the softmax gating and expert functions via partial differential equations. To address this issue, we propose using a novel class of modified softmax gating functions which transform the input value before delivering them to the gating functions. As a result, the previous interaction disappears and the parameter estimation rates are significantly improved.

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-nsigma, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-p, min-p) that inadvertently include more noise tokens at higher temperatures, top-nsigma maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-nsigma to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.

The pervasiveness of proprietary language models has raised privacy concerns for users' sensitive data, emphasizing the need for private inference (PI), where inference is performed directly on encrypted inputs. However, current PI methods face prohibitively higher communication and latency overheads, primarily due to nonlinear operations. In this paper, we present a comprehensive analysis to understand the role of nonlinearities in transformer-based decoder-only language models. We introduce AERO, a four-step architectural optimization framework that refines the existing LLM architecture for efficient PI by systematically removing nonlinearities such as LayerNorm and GELU and reducing FLOPs counts. For the first time, we propose a Softmax-only architecture with significantly fewer FLOPs tailored for efficient PI. Furthermore, we devise a novel entropy regularization technique to improve the performance of Softmax-only models. AERO achieves up to 4.23times communication and 1.94times latency reduction. We validate the effectiveness of AERO by benchmarking it against the state-of-the-art.

Understanding the parameter estimation of softmax gating Gaussian mixture of experts has remained a long-standing open problem in the literature. It is mainly due to three fundamental theoretical challenges associated with the softmax gating function: (i) the identifiability only up to the translation of parameters; (ii) the intrinsic interaction via partial differential equations between the softmax gating and the expert functions in the Gaussian density; (iii) the complex dependence between the numerator and denominator of the conditional density of softmax gating Gaussian mixture of experts. We resolve these challenges by proposing novel Voronoi loss functions among parameters and establishing the convergence rates of maximum likelihood estimator (MLE) for solving parameter estimation in these models. When the true number of experts is unknown and over-specified, our findings show a connection between the convergence rate of the MLE and a solvability problem of a system of polynomial equations.

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size n is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in R^K, where samples are assumed to be corrupted by a multi-variate additive Gaussian noise of an arbitrary magnitude. We prove the existence of an algorithm that with high probability outputs a simplex having a ell_2 distance of at most varepsilon from the true simplex (for any varepsilon>0). Also, we theoretically show that in order to achieve this bound, it is sufficient to have ngeleft(K^2/varepsilon^2right)e^{Omegaleft(K/SNR^2right)} samples, where SNR stands for the signal-to-noise ratio. This result solves an important open problem and shows as long as SNRgeOmegaleft(K^{1/2}right), the sample complexity of the noisy regime has the same order to that of the noiseless case. Our proofs are a combination of the so-called sample compression technique in ashtiani2018nearly, mathematical tools from high-dimensional geometry, and Fourier analysis. In particular, we have proposed a general Fourier-based technique for recovery of a more general class of distribution families from additive Gaussian noise, which can be further used in a variety of other related problems.

It is widely believed that noise conditioning is indispensable for denoising diffusion models to work successfully. This work challenges this belief. Motivated by research on blind image denoising, we investigate a variety of denoising-based generative models in the absence of noise conditioning. To our surprise, most models exhibit graceful degradation, and in some cases, they even perform better without noise conditioning. We provide a theoretical analysis of the error caused by removing noise conditioning and demonstrate that our analysis aligns with empirical observations. We further introduce a noise-unconditional model that achieves a competitive FID of 2.23 on CIFAR-10, significantly narrowing the gap to leading noise-conditional models. We hope our findings will inspire the community to revisit the foundations and formulations of denoising generative models.

We examine the problem of regret minimization when the learner is involved in a continuous game with other optimizing agents: in this case, if all players follow a no-regret algorithm, it is possible to achieve significantly lower regret relative to fully adversarial environments. We study this problem in the context of variationally stable games (a class of continuous games which includes all convex-concave and monotone games), and when the players only have access to noisy estimates of their individual payoff gradients. If the noise is additive, the game-theoretic and purely adversarial settings enjoy similar regret guarantees; however, if the noise is multiplicative, we show that the learners can, in fact, achieve constant regret. We achieve this faster rate via an optimistic gradient scheme with learning rate separation -- that is, the method's extrapolation and update steps are tuned to different schedules, depending on the noise profile. Subsequently, to eliminate the need for delicate hyperparameter tuning, we propose a fully adaptive method that attains nearly the same guarantees as its non-adapted counterpart, while operating without knowledge of either the game or of the noise profile.

With the rapid growth in model size, fine-tuning the large pre-trained language model has become increasingly difficult due to its extensive memory usage. Previous works usually focus on reducing the number of trainable parameters in the network. While the model parameters do contribute to memory usage, the primary memory bottleneck during training arises from storing feature maps, also known as activations, as they are crucial for gradient calculation. Notably, neural networks are usually trained using stochastic gradient descent. We argue that in stochastic optimization, models can handle noisy gradients as long as the gradient estimator is unbiased with reasonable variance. Following this motivation, we propose a new family of unbiased estimators called WTA-CRS, for matrix production with reduced variance, which only requires storing the sub-sampled activations for calculating the gradient. Our work provides both theoretical and experimental evidence that, in the context of tuning transformers, our proposed estimators exhibit lower variance compared to existing ones. By replacing the linear operation with our approximated one in transformers, we can achieve up to 2.7times peak memory reduction with almost no accuracy drop and enables up to 6.4times larger batch size. Under the same hardware, WTA-CRS enables better down-streaming task performance by applying larger models and/or faster training speed with larger batch sizes.

Top-K sparse softmax gating mixture of experts has been widely used for scaling up massive deep-learning architectures without increasing the computational cost. Despite its popularity in real-world applications, the theoretical understanding of that gating function has remained an open problem. The main challenge comes from the structure of the top-K sparse softmax gating function, which partitions the input space into multiple regions with distinct behaviors. By focusing on a Gaussian mixture of experts, we establish theoretical results on the effects of the top-K sparse softmax gating function on both density and parameter estimations. Our results hinge upon defining novel loss functions among parameters to capture different behaviors of the input regions. When the true number of experts k_{ast} is known, we demonstrate that the convergence rates of density and parameter estimations are both parametric on the sample size. However, when k_{ast} becomes unknown and the true model is over-specified by a Gaussian mixture of k experts where k > k_{ast}, our findings suggest that the number of experts selected from the top-K sparse softmax gating function must exceed the total cardinality of a certain number of Voronoi cells associated with the true parameters to guarantee the convergence of the density estimation. Moreover, while the density estimation rate remains parametric under this setting, the parameter estimation rates become substantially slow due to an intrinsic interaction between the softmax gating and expert functions.

Categorical variables are a natural choice for representing discrete structure in the world. However, stochastic neural networks rarely use categorical latent variables due to the inability to backpropagate through samples. In this work, we present an efficient gradient estimator that replaces the non-differentiable sample from a categorical distribution with a differentiable sample from a novel Gumbel-Softmax distribution. This distribution has the essential property that it can be smoothly annealed into a categorical distribution. We show that our Gumbel-Softmax estimator outperforms state-of-the-art gradient estimators on structured output prediction and unsupervised generative modeling tasks with categorical latent variables, and enables large speedups on semi-supervised classification.

Existing methods to recover model accuracy on analog-digital hardware in the presence of quantization and analog noise include noise-injection training. However, it can be slow in practice, incurring high computational costs, even when starting from pretrained models. We introduce the Sensitivity-Aware Finetuning (SAFT) approach that identifies noise sensitive layers in a model, and uses the information to freeze specific layers for noise-injection training. Our results show that SAFT achieves comparable accuracy to noise-injection training and is 2x to 8x faster.

We consider the two related problems of detecting if an example is misclassified or out-of-distribution. We present a simple baseline that utilizes probabilities from softmax distributions. Correctly classified examples tend to have greater maximum softmax probabilities than erroneously classified and out-of-distribution examples, allowing for their detection. We assess performance by defining several tasks in computer vision, natural language processing, and automatic speech recognition, showing the effectiveness of this baseline across all. We then show the baseline can sometimes be surpassed, demonstrating the room for future research on these underexplored detection tasks.

The complicated architecture and high training cost of vision transformers urge the exploration of post-training quantization. However, the heavy-tailed distribution of vision transformer activations hinders the effectiveness of previous post-training quantization methods, even with advanced quantizer designs. Instead of tuning the quantizer to better fit the complicated activation distribution, this paper proposes NoisyQuant, a quantizer-agnostic enhancement for the post-training activation quantization performance of vision transformers. We make a surprising theoretical discovery that for a given quantizer, adding a fixed Uniform noisy bias to the values being quantized can significantly reduce the quantization error under provable conditions. Building on the theoretical insight, NoisyQuant achieves the first success on actively altering the heavy-tailed activation distribution with additive noisy bias to fit a given quantizer. Extensive experiments show NoisyQuant largely improves the post-training quantization performance of vision transformer with minimal computation overhead. For instance, on linear uniform 6-bit activation quantization, NoisyQuant improves SOTA top-1 accuracy on ImageNet by up to 1.7%, 1.1% and 0.5% for ViT, DeiT, and Swin Transformer respectively, achieving on-par or even higher performance than previous nonlinear, mixed-precision quantization.

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently, diffusion models have been successfully employed for randomized smoothing to purify noise-perturbed samples before making predictions with a standard classifier. While these methods excel at small perturbation radii, they struggle with larger perturbations and incur a significant computational overhead during inference compared to classical methods. To address this, we reformulate the generative modeling task along the diffusion trajectories in pixel space as a discriminative task in the latent space. Specifically, we use instance discrimination to achieve consistent representations along the trajectories by aligning temporally adjacent points. After fine-tuning based on the learned representations, our model enables implicit denoising-then-classification via a single prediction, substantially reducing inference costs. We conduct extensive experiments on various datasets and achieve state-of-the-art performance with minimal computation budget during inference. For example, our method outperforms the certified accuracy of diffusion-based methods on ImageNet across all perturbation radii by 5.3% on average, with up to 11.6% at larger radii, while reducing inference costs by 85times on average. Codes are available at: https://github.com/jiachenlei/rRCM.

This paper tackles the problem of the heavy dependence of clean speech data required by deep learning based audio-denoising methods by showing that it is possible to train deep speech denoising networks using only noisy speech samples. Conventional wisdom dictates that in order to achieve good speech denoising performance, there is a requirement for a large quantity of both noisy speech samples and perfectly clean speech samples, resulting in a need for expensive audio recording equipment and extremely controlled soundproof recording studios. These requirements pose significant challenges in data collection, especially in economically disadvantaged regions and for low resource languages. This work shows that speech denoising deep neural networks can be successfully trained utilizing only noisy training audio. Furthermore it is revealed that such training regimes achieve superior denoising performance over conventional training regimes utilizing clean training audio targets, in cases involving complex noise distributions and low Signal-to-Noise ratios (high noise environments). This is demonstrated through experiments studying the efficacy of our proposed approach over both real-world noises and synthetic noises using the 20 layered Deep Complex U-Net architecture.

In this paper, we introduce a novel fine-tuning technique for language models, which involves incorporating symmetric noise into the embedding process. This method aims to enhance the model's function by more stringently regulating its local curvature, demonstrating superior performance over the current method, NEFTune. When fine-tuning the LLaMA-2-7B model using Alpaca, standard techniques yield a 29.79% score on AlpacaEval. However, our approach, SymNoise, increases this score significantly to 69.04%, using symmetric noisy embeddings. This is a 6.7% improvement over the state-of-the-art method, NEFTune~(64.69%). Furthermore, when tested on various models and stronger baseline instruction datasets, such as Evol-Instruct, ShareGPT, OpenPlatypus, SymNoise consistently outperforms NEFTune. The current literature, including NEFTune, has underscored the importance of more in-depth research into the application of noise-based strategies in the fine-tuning of language models. Our approach, SymNoise, is another significant step towards this direction, showing notable improvement over the existing state-of-the-art method.

While the numerous parameters in Large Language Models (LLMs) contribute to their superior performance, this massive scale makes them inefficient and memory-hungry. Thus, they are hard to deploy on commodity hardware, such as one single GPU. Given the memory and power constraints of such devices, model compression methods are widely employed to reduce both the model size and inference latency, which essentially trades off model quality in return for improved efficiency. Thus, optimizing this accuracy-efficiency trade-off is crucial for the LLM deployment on commodity hardware. In this paper, we introduce a new perspective to optimize this trade-off by prompting compressed models. Specifically, we first observe that for certain questions, the generation quality of a compressed LLM can be significantly improved by adding carefully designed hard prompts, though this isn't the case for all questions. Based on this observation, we propose a soft prompt learning method where we expose the compressed model to the prompt learning process, aiming to enhance the performance of prompts. Our experimental analysis suggests our soft prompt strategy greatly improves the performance of the 8x compressed LLaMA-7B model (with a joint 4-bit quantization and 50% weight pruning compression), allowing them to match their uncompressed counterparts on popular benchmarks. Also, we demonstrate that these learned prompts can be transferred across various datasets, tasks, and compression levels. Hence with this transferability, we can stitch the soft prompt to a newly compressed model to improve the test-time accuracy in an ``in-situ'' way.

Well-known activation functions like ReLU or Leaky ReLU are non-differentiable at the origin. Over the years, many smooth approximations of ReLU have been proposed using various smoothing techniques. We propose new smooth approximations of a non-differentiable activation function by convolving it with approximate identities. In particular, we present smooth approximations of Leaky ReLU and show that they outperform several well-known activation functions in various datasets and models. We call this function Smooth Activation Unit (SAU). Replacing ReLU by SAU, we get 5.12% improvement with ShuffleNet V2 (2.0x) model on CIFAR100 dataset.

Despite their ubiquity in language generation, it remains unknown why truncation sampling heuristics like nucleus sampling are so effective. We provide a theoretical explanation for the effectiveness of the truncation sampling by proving that truncation methods that discard tokens below some probability threshold (the most common type of truncation) can guarantee that all sampled tokens have nonzero true probability. However, thresholds are a coarse heuristic, and necessarily discard some tokens with nonzero true probability as well. In pursuit of a more precise sampling strategy, we show that we can leverage a known source of model errors, the softmax bottleneck, to prove that certain tokens have nonzero true probability, without relying on a threshold. Based on our findings, we develop an experimental truncation strategy and the present pilot studies demonstrating the promise of this type of algorithm. Our evaluations show that our method outperforms its threshold-based counterparts under automatic and human evaluation metrics for low-entropy (i.e., close to greedy) open-ended text generation. Our theoretical findings and pilot experiments provide both insight into why truncation sampling works, and make progress toward more expressive sampling algorithms that better surface the generative capabilities of large language models.

We present Simplex Random Features (SimRFs), a new random feature (RF) mechanism for unbiased approximation of the softmax and Gaussian kernels by geometrical correlation of random projection vectors. We prove that SimRFs provide the smallest possible mean square error (MSE) on unbiased estimates of these kernels among the class of weight-independent geometrically-coupled positive random feature (PRF) mechanisms, substantially outperforming the previously most accurate Orthogonal Random Features at no observable extra cost. We present a more computationally expensive SimRFs+ variant, which we prove is asymptotically optimal in the broader family of weight-dependent geometrical coupling schemes (which permit correlations between random vector directions and norms). In extensive empirical studies, we show consistent gains provided by SimRFs in settings including pointwise kernel estimation, nonparametric classification and scalable Transformers.

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.

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)).

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

A fundamental challenge for machine learning models is how to generalize learned models for out-of-distribution (OOD) data. Among various approaches, exploiting invariant features by Domain Adversarial Training (DAT) received widespread attention. Despite its success, we observe training instability from DAT, mostly due to over-confident domain discriminator and environment label noise. To address this issue, we proposed Environment Label Smoothing (ELS), which encourages the discriminator to output soft probability, which thus reduces the confidence of the discriminator and alleviates the impact of noisy environment labels. We demonstrate, both experimentally and theoretically, that ELS can improve training stability, local convergence, and robustness to noisy environment labels. By incorporating ELS with DAT methods, we are able to yield state-of-art results on a wide range of domain generalization/adaptation tasks, particularly when the environment labels are highly noisy.

Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems. Despite its tremendous empirical success, the rigorous theoretical understanding of why unsupervised pretraining generally helps remains rather limited -- most existing results are restricted to particular methods or approaches for unsupervised pretraining with specialized structural assumptions. This paper studies a generic framework, where the unsupervised representation learning task is specified by an abstract class of latent variable models Phi and the downstream task is specified by a class of prediction functions Psi. We consider a natural approach of using Maximum Likelihood Estimation (MLE) for unsupervised pretraining and Empirical Risk Minimization (ERM) for learning downstream tasks. We prove that, under a mild ''informative'' condition, our algorithm achieves an excess risk of mathcal{O}(mathcal{C_Phi/m} + mathcal{C_Psi/n}) for downstream tasks, where C_Phi, C_Psi are complexity measures of function classes Phi, Psi, and m, n are the number of unlabeled and labeled data respectively. Comparing to the baseline of mathcal{O}(mathcal{C_{Phi circ Psi}/n}) achieved by performing supervised learning using only the labeled data, our result rigorously shows the benefit of unsupervised pretraining when m gg n and C_{Phicirc Psi} > C_Psi. This paper further shows that our generic framework covers a wide range of approaches for unsupervised pretraining, including factor models, Gaussian mixture models, and contrastive learning.

Self-training is a well-known approach for semi-supervised learning. It consists of iteratively assigning pseudo-labels to unlabeled data for which the model is confident and treating them as labeled examples. For neural networks, softmax prediction probabilities are often used as a confidence measure, although they are known to be overconfident, even for wrong predictions. This phenomenon is particularly intensified in the presence of sample selection bias, i.e., when data labeling is subject to some constraint. To address this issue, we propose a novel confidence measure, called T-similarity, built upon the prediction diversity of an ensemble of linear classifiers. We provide the theoretical analysis of our approach by studying stationary points and describing the relationship between the diversity of the individual members and their performance. We empirically demonstrate the benefit of our confidence measure for three different pseudo-labeling policies on classification datasets of various data modalities. The code is available at https://github.com/ambroiseodt/tsim.

As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the entire vocabulary can be simplified, giving speedups compared to the baseline. A problem we notice about the current landscape of such sampling methods is the lack of a systematic comparison and some myths about preferring one over another. In this work, we consider Monte Carlo sampling, importance sampling, a novel method we call compensated partial summation, and noise contrastive estimation. Linking back to the three traditional criteria, namely mean squared error, binary cross-entropy, and cross-entropy, we derive the theoretical solutions to the training problems. Contrary to some common belief, we show that all these sampling methods can perform equally well, as long as we correct for the intended class posterior probabilities. Experimental results in language modeling and automatic speech recognition on Switchboard and LibriSpeech support our claim, with all sampling-based methods showing similar perplexities and word error rates while giving the expected speedups.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. [2022] as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance sigma_{1:T}^2 and the cumulative adversarial variation Sigma_{1:T}^2 for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance sigma_{max}^2 and the maximal adversarial variation Sigma_{max}^2 for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model. For convex and smooth functions, we obtain the same O(sigma_{1:T^2}+Sigma_{1:T^2}) regret bound, without the convexity requirement of individual functions. For strongly convex and smooth functions, we establish an O(min{log (sigma_{1:T}^2+Sigma_{1:T}^2), (sigma_{max}^2 + Sigma_{max}^2) log T}) bound, better than their O((sigma_{max}^2 + Sigma_{max}^2) log T) bound. For exp-concave and smooth functions, we achieve a new O(dlog(sigma_{1:T}^2+Sigma_{1:T}^2)) bound. Owing to the OMD framework, we can further extend our result to obtain dynamic regret guarantees, which are more favorable in non-stationary online scenarios. The attained results allow us to recover excess risk bounds of the stochastic setting and regret bounds of the adversarial setting, and derive new guarantees for many intermediate scenarios.

Enhancing the visibility in extreme low-light environments is a challenging task. Under nearly lightless condition, existing image denoising methods could easily break down due to significantly low SNR. In this paper, we systematically study the noise statistics in the imaging pipeline of CMOS photosensors, and formulate a comprehensive noise model that can accurately characterize the real noise structures. Our novel model considers the noise sources caused by digital camera electronics which are largely overlooked by existing methods yet have significant influence on raw measurement in the dark. It provides a way to decouple the intricate noise structure into different statistical distributions with physical interpretations. Moreover, our noise model can be used to synthesize realistic training data for learning-based low-light denoising algorithms. In this regard, although promising results have been shown recently with deep convolutional neural networks, the success heavily depends on abundant noisy clean image pairs for training, which are tremendously difficult to obtain in practice. Generalizing their trained models to images from new devices is also problematic. Extensive experiments on multiple low-light denoising datasets -- including a newly collected one in this work covering various devices -- show that a deep neural network trained with our proposed noise formation model can reach surprisingly-high accuracy. The results are on par with or sometimes even outperform training with paired real data, opening a new door to real-world extreme low-light photography.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

Soft prompt tuning achieves superior performances across a wide range of few-shot tasks. However, the performances of prompt tuning can be highly sensitive to the initialization of the prompts. We also empirically observe that conventional prompt tuning methods cannot encode and learn sufficient task-relevant information from prompt tokens. In this work, we develop an information-theoretic framework that formulates soft prompt tuning as maximizing mutual information between prompts and other model parameters (or encoded representations). This novel view helps us to develop a more efficient, accurate and robust soft prompt tuning method InfoPrompt. With this framework, we develop two novel mutual information based loss functions, to (i) discover proper prompt initialization for the downstream tasks and learn sufficient task-relevant information from prompt tokens and (ii) encourage the output representation from the pretrained language model to be more aware of the task-relevant information captured in the learnt prompt. Extensive experiments validate that InfoPrompt can significantly accelerate the convergence of the prompt tuning and outperform traditional prompt tuning methods. Finally, we provide a formal theoretical result for showing to show that gradient descent type algorithm can be used to train our mutual information loss.

Inspired by Regularized Lottery Ticket Hypothesis (RLTH), which hypothesizes that there exist smooth (non-binary) subnetworks within a dense network that achieve the competitive performance of the dense network, we propose a few-shot class incremental learning (FSCIL) method referred to as Soft-SubNetworks (SoftNet). Our objective is to learn a sequence of sessions incrementally, where each session only includes a few training instances per class while preserving the knowledge of the previously learned ones. SoftNet jointly learns the model weights and adaptive non-binary soft masks at a base training session in which each mask consists of the major and minor subnetwork; the former aims to minimize catastrophic forgetting during training, and the latter aims to avoid overfitting to a few samples in each new training session. We provide comprehensive empirical validations demonstrating that our SoftNet effectively tackles the few-shot incremental learning problem by surpassing the performance of state-of-the-art baselines over benchmark datasets.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

While deep convolutional neural networks (CNNs) have achieved impressive success in image denoising with additive white Gaussian noise (AWGN), their performance remains limited on real-world noisy photographs. The main reason is that their learned models are easy to overfit on the simplified AWGN model which deviates severely from the complicated real-world noise model. In order to improve the generalization ability of deep CNN denoisers, we suggest training a convolutional blind denoising network (CBDNet) with more realistic noise model and real-world noisy-clean image pairs. On the one hand, both signal-dependent noise and in-camera signal processing pipeline is considered to synthesize realistic noisy images. On the other hand, real-world noisy photographs and their nearly noise-free counterparts are also included to train our CBDNet. To further provide an interactive strategy to rectify denoising result conveniently, a noise estimation subnetwork with asymmetric learning to suppress under-estimation of noise level is embedded into CBDNet. Extensive experimental results on three datasets of real-world noisy photographs clearly demonstrate the superior performance of CBDNet over state-of-the-arts in terms of quantitative metrics and visual quality. The code has been made available at https://github.com/GuoShi28/CBDNet.

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on access to it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recent works proposing solutions for learning from instance-dependent noisy labels, the field lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix for the generic case at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result also reveals that disentangled features are helpful in the above identification task and we provide empirical evidence.

The volume of "free" data on the internet has been key to the current success of deep learning. However, it also raises privacy concerns about the unauthorized exploitation of personal data for training commercial models. It is thus crucial to develop methods to prevent unauthorized data exploitation. This paper raises the question: can data be made unlearnable for deep learning models? We present a type of error-minimizing noise that can indeed make training examples unlearnable. Error-minimizing noise is intentionally generated to reduce the error of one or more of the training example(s) close to zero, which can trick the model into believing there is "nothing" to learn from these example(s). The noise is restricted to be imperceptible to human eyes, and thus does not affect normal data utility. We empirically verify the effectiveness of error-minimizing noise in both sample-wise and class-wise forms. We also demonstrate its flexibility under extensive experimental settings and practicability in a case study of face recognition. Our work establishes an important first step towards making personal data unexploitable to deep learning models.

Misclassification detection is an important problem in machine learning, as it allows for the identification of instances where the model's predictions are unreliable. However, conventional uncertainty measures such as Shannon entropy do not provide an effective way to infer the real uncertainty associated with the model's predictions. In this paper, we introduce a novel data-driven measure of uncertainty relative to an observer for misclassification detection. By learning patterns in the distribution of soft-predictions, our uncertainty measure can identify misclassified samples based on the predicted class probabilities. Interestingly, according to the proposed measure, soft-predictions corresponding to misclassified instances can carry a large amount of uncertainty, even though they may have low Shannon entropy. We demonstrate empirical improvements over multiple image classification tasks, outperforming state-of-the-art misclassification detection methods.

Label noise is one of the key factors that lead to the poor generalization of deep learning models. Existing label-noise learning methods usually assume that the ground-truth classes of the training data are balanced. However, the real-world data is often imbalanced, leading to the inconsistency between observed and intrinsic class distribution with label noises. In this case, it is hard to distinguish clean samples from noisy samples on the intrinsic tail classes with the unknown intrinsic class distribution. In this paper, we propose a learning framework for label-noise learning with intrinsically long-tailed data. Specifically, we propose two-stage bi-dimensional sample selection (TABASCO) to better separate clean samples from noisy samples, especially for the tail classes. TABASCO consists of two new separation metrics that complement each other to compensate for the limitation of using a single metric in sample separation. Extensive experiments on benchmarks demonstrate the effectiveness of our method. Our code is available at https://github.com/Wakings/TABASCO.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Sample selection is a prevalent method in learning with noisy labels, where small-loss data are typically considered as correctly labeled data. However, this method may not effectively identify clean hard examples with large losses, which are critical for achieving the model's close-to-optimal generalization performance. In this paper, we propose a new framework, Late Stopping, which leverages the intrinsic robust learning ability of DNNs through a prolonged training process. Specifically, Late Stopping gradually shrinks the noisy dataset by removing high-probability mislabeled examples while retaining the majority of clean hard examples in the training set throughout the learning process. We empirically observe that mislabeled and clean examples exhibit differences in the number of epochs required for them to be consistently and correctly classified, and thus high-probability mislabeled examples can be removed. Experimental results on benchmark-simulated and real-world noisy datasets demonstrate that the proposed method outperforms state-of-the-art counterparts.

We consider the neural contextual bandit problem. In contrast to the existing work which primarily focuses on ReLU neural nets, we consider a general set of smooth activation functions. Under this more general setting, (i) we derive non-asymptotic error bounds on the difference between an overparameterized neural net and its corresponding neural tangent kernel, (ii) we propose an algorithm with a provably sublinear regret bound that is also efficient in the finite regime as demonstrated by empirical studies. The non-asymptotic error bounds may be of broader interest as a tool to establish the relation between the smoothness of the activation functions in neural contextual bandits and the smoothness of the kernels in kernel bandits.

Recent advances in large language models (LLMs) have promoted generative error correction (GER) for automatic speech recognition (ASR), which leverages the rich linguistic knowledge and powerful reasoning ability of LLMs to improve recognition results. The latest work proposes a GER benchmark with HyPoradise dataset to learn the mapping from ASR N-best hypotheses to ground-truth transcription by efficient LLM finetuning, which shows great effectiveness but lacks specificity on noise-robust ASR. In this work, we extend the benchmark to noisy conditions and investigate if we can teach LLMs to perform denoising for GER just like what robust ASR do}, where one solution is introducing noise information as a conditioner into LLM. However, directly incorporating noise embeddings from audio encoder could harm the LLM tuning due to cross-modality gap. To this end, we propose to extract a language-space noise embedding from the N-best list to represent the noise conditions of source speech, which can promote the denoising process in GER. Furthermore, in order to enhance its representation ability of audio noise, we design a knowledge distillation (KD) approach via mutual information estimation to distill the real noise information in audio embeddings to our language embedding. Experiments on various latest LLMs demonstrate our approach achieves a new breakthrough with up to 53.9% correction improvement in terms of word error rate while with limited training data. Analysis shows that our language-space noise embedding can well represent the noise conditions of source speech, under which off-the-shelf LLMs show strong ability of language-space denoising.

Conditional diffusion models have shown remarkable performance in various generative tasks, but training them requires large-scale datasets that often contain noise in conditional inputs, a.k.a. noisy labels. This noise leads to condition mismatch and quality degradation of generated data. This paper proposes Transition-aware weighted Denoising Score Matching (TDSM) for training conditional diffusion models with noisy labels, which is the first study in the line of diffusion models. The TDSM objective contains a weighted sum of score networks, incorporating instance-wise and time-dependent label transition probabilities. We introduce a transition-aware weight estimator, which leverages a time-dependent noisy-label classifier distinctively customized to the diffusion process. Through experiments across various datasets and noisy label settings, TDSM improves the quality of generated samples aligned with given conditions. Furthermore, our method improves generation performance even on prevalent benchmark datasets, which implies the potential noisy labels and their risk of generative model learning. Finally, we show the improved performance of TDSM on top of conventional noisy label corrections, which empirically proving its contribution as a part of label-noise robust generative models. Our code is available at: https://github.com/byeonghu-na/tdsm.

We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum ell_2-norm interpolant, we show that randomly initialized deep linear networks can closely approximate or even match known bounds for the minimum ell_2-norm interpolant. Our analysis also reveals that interpolating deep linear models have exactly the same conditional variance as the minimum ell_2-norm solution. Since the noise affects the excess risk only through the conditional variance, this implies that depth does not improve the algorithm's ability to "hide the noise". Our simulations verify that aspects of our bounds reflect typical behavior for simple data distributions. We also find that similar phenomena are seen in simulations with ReLU networks, although the situation there is more nuanced.

Deep neural networks trained on large supervised datasets have led to impressive results in image classification and other tasks. However, well-annotated datasets can be time-consuming and expensive to collect, lending increased interest to larger but noisy datasets that are more easily obtained. In this paper, we show that deep neural networks are capable of generalizing from training data for which true labels are massively outnumbered by incorrect labels. We demonstrate remarkably high test performance after training on corrupted data from MNIST, CIFAR, and ImageNet. For example, on MNIST we obtain test accuracy above 90 percent even after each clean training example has been diluted with 100 randomly-labeled examples. Such behavior holds across multiple patterns of label noise, even when erroneous labels are biased towards confusing classes. We show that training in this regime requires a significant but manageable increase in dataset size that is related to the factor by which correct labels have been diluted. Finally, we provide an analysis of our results that shows how increasing noise decreases the effective batch size.

Learning from preference-based feedback has recently gained traction as a promising approach to align language models with human interests. While these aligned generative models have demonstrated impressive capabilities across various tasks, their dependence on high-quality human preference data poses a bottleneck in practical applications. Specifically, noisy (incorrect and ambiguous) preference pairs in the dataset might restrict the language models from capturing human intent accurately. While practitioners have recently proposed heuristics to mitigate the effect of noisy preferences, a complete theoretical understanding of their workings remain elusive. In this work, we aim to bridge this gap by by introducing a general framework for policy optimization in the presence of random preference flips. We focus on the direct preference optimization (DPO) algorithm in particular since it assumes that preferences adhere to the Bradley-Terry-Luce (BTL) model, raising concerns about the impact of noisy data on the learned policy. We design a novel loss function, which de-bias the effect of noise on average, making a policy trained by minimizing that loss robust to the noise. Under log-linear parameterization of the policy class and assuming good feature coverage of the SFT policy, we prove that the sub-optimality gap of the proposed robust DPO (rDPO) policy compared to the optimal policy is of the order O(1{1-2epsilon}frac{d{n}}), where epsilon < 1/2 is flip rate of labels, d is policy parameter dimension and n is size of dataset. Our experiments on IMDb sentiment generation and Anthropic's helpful-harmless dataset show that rDPO is robust to noise in preference labels compared to vanilla DPO and other heuristics proposed by practitioners.

Implicit feedback data is extensively explored in recommendation as it is easy to collect and generally applicable. However, predicting users' preference on implicit feedback data is a challenging task since we can only observe positive (voted) samples and unvoted samples. It is difficult to distinguish between the negative samples and unlabeled positive samples from the unvoted ones. Existing works, such as Bayesian Personalized Ranking (BPR), sample unvoted items as negative samples uniformly, therefore suffer from a critical noisy-label issue. To address this gap, we design an adaptive sampler based on noisy-label robust learning for implicit feedback data. To formulate the issue, we first introduce Bayesian Point-wise Optimization (BPO) to learn a model, e.g., Matrix Factorization (MF), by maximum likelihood estimation. We predict users' preferences with the model and learn it by maximizing likelihood of observed data labels, i.e., a user prefers her positive samples and has no interests in her unvoted samples. However, in reality, a user may have interests in some of her unvoted samples, which are indeed positive samples mislabeled as negative ones. We then consider the risk of these noisy labels, and propose a Noisy-label Robust BPO (NBPO). NBPO also maximizes the observation likelihood while connects users' preference and observed labels by the likelihood of label flipping based on the Bayes' theorem. In NBPO, a user prefers her true positive samples and shows no interests in her true negative samples, hence the optimization quality is dramatically improved. Extensive experiments on two public real-world datasets show the significant improvement of our proposed optimization methods.

Leveraging privileged information (PI), or features available during training but not at test time, has recently been shown to be an effective method for addressing label noise. However, the reasons for its effectiveness are not well understood. In this study, we investigate the role played by different properties of the PI in explaining away label noise. Through experiments on multiple datasets with real PI (CIFAR-N/H) and a new large-scale benchmark ImageNet-PI, we find that PI is most helpful when it allows networks to easily distinguish clean from noisy data, while enabling a learning shortcut to memorize the noisy examples. Interestingly, when PI becomes too predictive of the target label, PI methods often perform worse than their no-PI baselines. Based on these findings, we propose several enhancements to the state-of-the-art PI methods and demonstrate the potential of PI as a means of tackling label noise. Finally, we show how we can easily combine the resulting PI approaches with existing no-PI techniques designed to deal with label noise.

In this paper, we study the problem of learning image classification models in the presence of label noise. We revisit a simple compression regularization named Nested Dropout. We find that Nested Dropout, though originally proposed to perform fast information retrieval and adaptive data compression, can properly regularize a neural network to combat label noise. Moreover, owing to its simplicity, it can be easily combined with Co-teaching to further boost the performance. Our final model remains simple yet effective: it achieves comparable or even better performance than the state-of-the-art approaches on two real-world datasets with label noise which are Clothing1M and ANIMAL-10N. On Clothing1M, our approach obtains 74.9% accuracy which is slightly better than that of DivideMix. On ANIMAL-10N, we achieve 84.1% accuracy while the best public result by PLC is 83.4%. We hope that our simple approach can be served as a strong baseline for learning with label noise. Our implementation is available at https://github.com/yingyichen-cyy/Nested-Co-teaching.

In the presence of noisy labels, designing robust loss functions is critical for securing the generalization performance of deep neural networks. Cross Entropy (CE) loss has been shown to be not robust to noisy labels due to its unboundedness. To alleviate this issue, existing works typically design specialized robust losses with the symmetric condition, which usually lead to the underfitting issue. In this paper, our key idea is to induce a loss bound at the logit level, thus universally enhancing the noise robustness of existing losses. Specifically, we propose logit clipping (LogitClip), which clamps the norm of the logit vector to ensure that it is upper bounded by a constant. In this manner, CE loss equipped with our LogitClip method is effectively bounded, mitigating the overfitting to examples with noisy labels. Moreover, we present theoretical analyses to certify the noise-tolerant ability of LogitClip. Extensive experiments show that LogitClip not only significantly improves the noise robustness of CE loss, but also broadly enhances the generalization performance of popular robust losses.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

We present Noisy Student Training, a semi-supervised learning approach that works well even when labeled data is abundant. Noisy Student Training achieves 88.4% top-1 accuracy on ImageNet, which is 2.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 61.0% to 83.7%, reduces ImageNet-C mean corruption error from 45.7 to 28.3, and reduces ImageNet-P mean flip rate from 27.8 to 12.2. Noisy Student Training extends the idea of self-training and distillation with the use of equal-or-larger student models and noise added to the student during learning. On ImageNet, we first train an EfficientNet model on labeled images and use it as a teacher to generate pseudo labels for 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the learning of the student, we inject noise such as dropout, stochastic depth, and data augmentation via RandAugment to the student so that the student generalizes better than the teacher. Models are available at https://github.com/tensorflow/tpu/tree/master/models/official/efficientnet. Code is available at https://github.com/google-research/noisystudent.

Mixture of Experts (MoE) architectures have recently started burgeoning due to their ability to scale model's capacity while maintaining the computational cost affordable. Furthermore, they can be applied to both Transformers and State Space Models, the current state-of-the-art models in numerous fields. While MoE has been mostly investigated for the pre-training stage, its use in parameter-efficient transfer learning settings is under-explored. To narrow this gap, this paper attempts to demystify the use of MoE for parameter-efficient fine-tuning of Audio Spectrogram Transformers to audio and speech downstream tasks. Specifically, we propose Soft Mixture of Adapters (Soft-MoA). It exploits adapters as the experts and, leveraging the recent Soft MoE method, it relies on a soft assignment between the input tokens and experts to keep the computational time limited. Extensive experiments across 4 benchmarks demonstrate that Soft-MoA outperforms the single adapter method and performs on par with the dense MoA counterpart. We finally present ablation studies on key elements of Soft-MoA, showing for example that Soft-MoA achieves better scaling with more experts, as well as ensuring that all experts contribute to the computation of the output tokens, thus dispensing with the expert imbalance issue.

Recent works have shown that deep neural networks are vulnerable to adversarial examples that find samples close to the original image but can make the model misclassify. Even with access only to the model's output, an attacker can employ black-box attacks to generate such adversarial examples. In this work, we propose a simple and lightweight defense against black-box attacks by adding random noise to hidden features at intermediate layers of the model at inference time. Our theoretical analysis confirms that this method effectively enhances the model's resilience against both score-based and decision-based black-box attacks. Importantly, our defense does not necessitate adversarial training and has minimal impact on accuracy, rendering it applicable to any pre-trained model. Our analysis also reveals the significance of selectively adding noise to different parts of the model based on the gradient of the adversarial objective function, which can be varied during the attack. We demonstrate the robustness of our defense against multiple black-box attacks through extensive empirical experiments involving diverse models with various architectures.

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

Pre-training on large-scale datasets and then fine-tuning on downstream tasks have become a standard practice in deep learning. However, pre-training data often contain label noise that may adversely affect the generalization of the model. This paper aims to understand the nature of noise in pre-training datasets and to mitigate its impact on downstream tasks. More specifically, through extensive experiments of supervised pre-training models on synthetic noisy ImageNet-1K and YFCC15M datasets, we demonstrate that while slight noise in pre-training can benefit in-domain (ID) transfer performance, where the training and testing data share the same distribution, it always deteriorates out-of-domain (OOD) performance, where training and testing data distribution are different. We empirically verify that the reason behind is noise in pre-training shapes the feature space differently. We then propose a light-weight black-box tuning method (NMTune) to affine the feature space to mitigate the malignant effect of noise and improve generalization on both ID and OOD tasks, considering one may not be able to fully fine-tune or even access the pre-trained models. We conduct practical experiments on popular vision and language models that are pre-trained on noisy data for evaluation of our approach. Our analysis and results show the importance of this interesting and novel research direction, which we term Noisy Model Learning.

Dense-to-sparse gating mixture of experts (MoE) has recently become an effective alternative to a well-known sparse MoE. Rather than fixing the number of activated experts as in the latter model, which could limit the investigation of potential experts, the former model utilizes the temperature to control the softmax weight distribution and the sparsity of the MoE during training in order to stabilize the expert specialization. Nevertheless, while there are previous attempts to theoretically comprehend the sparse MoE, a comprehensive analysis of the dense-to-sparse gating MoE has remained elusive. Therefore, we aim to explore the impacts of the dense-to-sparse gate on the maximum likelihood estimation under the Gaussian MoE in this paper. We demonstrate that due to interactions between the temperature and other model parameters via some partial differential equations, the convergence rates of parameter estimations are slower than any polynomial rates, and could be as slow as O(1/log(n)), where n denotes the sample size. To address this issue, we propose using a novel activation dense-to-sparse gate, which routes the output of a linear layer to an activation function before delivering them to the softmax function. By imposing linearly independence conditions on the activation function and its derivatives, we show that the parameter estimation rates are significantly improved to polynomial rates.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Black box optimisation of an unknown function from expensive and noisy evaluations is a ubiquitous problem in machine learning, academic research and industrial production. An abstraction of the problem can be formulated as a kernel based bandit problem (also known as Bayesian optimisation), where a learner aims at optimising a kernelized function through sequential noisy observations. The existing work predominantly assumes feedback is immediately available; an assumption which fails in many real world situations, including recommendation systems, clinical trials and hyperparameter tuning. We consider a kernel bandit problem under stochastically delayed feedback, and propose an algorithm with mathcal{O}(Gamma_k(T)T+E[tau]) regret, where T is the number of time steps, Gamma_k(T) is the maximum information gain of the kernel with T observations, and tau is the delay random variable. This represents a significant improvement over the state of the art regret bound of mathcal{O}(Gamma_k(T)T+E[tau]Gamma_k(T)) reported in Verma et al. (2022). In particular, for very non-smooth kernels, the information gain grows almost linearly in time, trivializing the existing results. We also validate our theoretical results with simulations.

We present a state-of-the-art speech recognition system developed using end-to-end deep learning. Our architecture is significantly simpler than traditional speech systems, which rely on laboriously engineered processing pipelines; these traditional systems also tend to perform poorly when used in noisy environments. In contrast, our system does not need hand-designed components to model background noise, reverberation, or speaker variation, but instead directly learns a function that is robust to such effects. We do not need a phoneme dictionary, nor even the concept of a "phoneme." Key to our approach is a well-optimized RNN training system that uses multiple GPUs, as well as a set of novel data synthesis techniques that allow us to efficiently obtain a large amount of varied data for training. Our system, called Deep Speech, outperforms previously published results on the widely studied Switchboard Hub5'00, achieving 16.0% error on the full test set. Deep Speech also handles challenging noisy environments better than widely used, state-of-the-art commercial speech systems.

Label Smoothing (LS) is widely adopted to curb overconfidence in neural network predictions and enhance generalization. However, previous research shows that LS can force feature representations into excessively tight clusters, eroding intra-class distinctions. More recent findings suggest that LS also induces overconfidence in misclassifications, yet the precise mechanism remained unclear. In this work, we decompose the loss term introduced by LS, revealing two key components: (i) a regularization term that functions only when the prediction is correct, and (ii) an error-enhancement term that emerges under misclassifications. This latter term compels the model to reinforce incorrect predictions with exaggerated certainty, further collapsing the feature space. To address these issues, we propose Max Suppression (MaxSup), which uniformly applies the intended regularization to both correct and incorrect predictions by penalizing the top-1 logit instead of the ground-truth logit. Through feature analyses, we show that MaxSup restores intra-class variation and sharpens inter-class boundaries. Extensive experiments on image classification and downstream tasks confirm that MaxSup is a more robust alternative to LS. Code is available at: https://github.com/ZhouYuxuanYX/Maximum-Suppression-Regularization.

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to learn high-level semantic relationships, resulting in sub-optimal performance. To address this issue, image augmentation strategies are employed as regularization techniques. While additive noise input during network training is a well-established augmentation as regularization method, modern pipelines often favor more robust techniques such as dropout and weight decay. This preference stems from the observation that combining these established techniques with noise input can adversely affect model performance. In this study, we propose a novel pretraining pipeline that learns to generate conditional noise mask specifically tailored to improve performance on multi-modal and multi-organ datasets. As a reinforcement learning algorithm, our approach employs a dual-component system comprising a very light-weight policy network that learns to sample conditional noise using a differentiable beta distribution as well as a classifier network. The policy network is trained using the reinforce algorithm to generate image-specific noise masks that regularize the classifier during pretraining. A key aspect is that the policy network's role is limited to obtaining an intermediate (or heated) model before fine-tuning. During inference, the policy network is omitted, allowing direct comparison between the baseline and noise-regularized models. We conducted experiments and related analyses on RadImageNet datasets. Results demonstrate that fine-tuning the intermediate models consistently outperforms conventional training algorithms on both classification and generalization to unseen concept tasks.

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity bounds are more accurate and less studied than in-expectation ones. However, SOTA high-probability non-asymptotic convergence results are derived under strong assumptions such as the boundedness of the gradient noise variance or of the objective's gradient itself. In this paper, we propose several algorithms with high-probability convergence results under less restrictive assumptions. In particular, we derive new high-probability convergence results under the assumption that the gradient/operator noise has bounded central alpha-th moment for alpha in (1,2] in the following setups: (i) smooth non-convex / Polyak-Lojasiewicz / convex / strongly convex / quasi-strongly convex minimization problems, (ii) Lipschitz / star-cocoercive and monotone / quasi-strongly monotone variational inequalities. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes studied in stochastic optimization.

Face recognition has been an active and vital topic among computer vision community for a long time. Previous researches mainly focus on loss functions used for facial feature extraction network, among which the improvements of softmax-based loss functions greatly promote the performance of face recognition. However, the contradiction between the drastically increasing number of face identities and the shortage of GPU memories is gradually becoming irreconcilable. In this paper, we thoroughly analyze the optimization goal of softmax-based loss functions and the difficulty of training massive identities. We find that the importance of negative classes in softmax function in face representation learning is not as high as we previously thought. The experiment demonstrates no loss of accuracy when training with only 10\% randomly sampled classes for the softmax-based loss functions, compared with training with full classes using state-of-the-art models on mainstream benchmarks. We also implement a very efficient distributed sampling algorithm, taking into account model accuracy and training efficiency, which uses only eight NVIDIA RTX2080Ti to complete classification tasks with tens of millions of identities. The code of this paper has been made available https://github.com/deepinsight/insightface/tree/master/recognition/partial_fc.

Fine-tuning large pretrained language models on a limited training corpus usually suffers from poor generalization. Prior works show that the recently-proposed sharpness-aware minimization (SAM) optimization method can improve the model generalization. However, SAM adds a perturbation to each model parameter equally (but not all parameters contribute equally to the optimization of training), which we argue is sub-optimal and will lead to excessive computation. In this paper, we propose a novel optimization procedure, namely FSAM, which introduces a Fisher mask to improve the efficiency and performance of SAM. In short, instead of adding perturbation to all parameters, FSAM uses the Fisher information to identity the important parameters and formulates a Fisher mask to obtain the sparse perturbation, i.e., making the optimizer focus on these important parameters. Experiments on various tasks in GLUE and SuperGLUE benchmarks show that FSAM consistently outperforms the vanilla SAM by 0.67~1.98 average score among four different pretrained models. We also empirically show that FSAM works well in other complex scenarios, e.g., fine-tuning on generation tasks or limited training data. Encouragingly, when training data is limited, FSAM improves the SAM by a large margin, i.e., up to 15.1.

Recently, deep neural networks such as RNN, CNN and Transformer have been applied in the task of sequential recommendation, which aims to capture the dynamic preference characteristics from logged user behavior data for accurate recommendation. However, in online platforms, logged user behavior data is inevitable to contain noise, and deep recommendation models are easy to overfit on these logged data. To tackle this problem, we borrow the idea of filtering algorithms from signal processing that attenuates the noise in the frequency domain. In our empirical experiments, we find that filtering algorithms can substantially improve representative sequential recommendation models, and integrating simple filtering algorithms (eg Band-Stop Filter) with an all-MLP architecture can even outperform competitive Transformer-based models. Motivated by it, we propose FMLP-Rec, an all-MLP model with learnable filters for sequential recommendation task. The all-MLP architecture endows our model with lower time complexity, and the learnable filters can adaptively attenuate the noise information in the frequency domain. Extensive experiments conducted on eight real-world datasets demonstrate the superiority of our proposed method over competitive RNN, CNN, GNN and Transformer-based methods. Our code and data are publicly available at the link: blue{https://github.com/RUCAIBox/FMLP-Rec}.

Unsupervised denoising is a crucial challenge in real-world imaging applications. Unsupervised deep-learning methods have demonstrated impressive performance on benchmarks based on synthetic noise. However, no metrics are available to evaluate these methods in an unsupervised fashion. This is highly problematic for the many practical applications where ground-truth clean images are not available. In this work, we propose two novel metrics: the unsupervised mean squared error (MSE) and the unsupervised peak signal-to-noise ratio (PSNR), which are computed using only noisy data. We provide a theoretical analysis of these metrics, showing that they are asymptotically consistent estimators of the supervised MSE and PSNR. Controlled numerical experiments with synthetic noise confirm that they provide accurate approximations in practice. We validate our approach on real-world data from two imaging modalities: videos in raw format and transmission electron microscopy. Our results demonstrate that the proposed metrics enable unsupervised evaluation of denoising methods based exclusively on noisy data.

Uncertainty sampling in active learning is heavily used in practice to reduce the annotation cost. However, there has been no wide consensus on the function to be used for uncertainty estimation in binary classification tasks and convergence guarantees of the corresponding active learning algorithms are not well understood. The situation is even more challenging for multi-category classification. In this work, we propose an efficient uncertainty estimator for binary classification which we also extend to multiple classes, and provide a non-asymptotic rate of convergence for our uncertainty sampling-based active learning algorithm in both cases under no-noise conditions (i.e., linearly separable data). We also extend our analysis to the noisy case and provide theoretical guarantees for our algorithm under the influence of noise in the task of binary and multi-class classification.

With the growth of model and data sizes, a broad effort has been made to design pruning techniques that reduce the resource demand of deep learning pipelines, while retaining model performance. In order to reduce both inference and training costs, a prominent line of work uses low-rank matrix factorizations to represent the network weights. Although able to retain accuracy, we observe that low-rank methods tend to compromise model robustness against adversarial perturbations. By modeling robustness in terms of the condition number of the neural network, we argue that this loss of robustness is due to the exploding singular values of the low-rank weight matrices. Thus, we introduce a robust low-rank training algorithm that maintains the network's weights on the low-rank matrix manifold while simultaneously enforcing approximate orthonormal constraints. The resulting model reduces both training and inference costs while ensuring well-conditioning and thus better adversarial robustness, without compromising model accuracy. This is shown by extensive numerical evidence and by our main approximation theorem that shows the computed robust low-rank network well-approximates the ideal full model, provided a highly performing low-rank sub-network exists.

In this work, we theoretically investigate the generalization properties of neural networks (NN) trained by stochastic gradient descent (SGD) algorithm with large learning rates. Under such a training regime, our finding is that, the oscillation of the NN weights caused by the large learning rate SGD training turns out to be beneficial to the generalization of the NN, which potentially improves over the same NN trained by SGD with small learning rates that converges more smoothly. In view of this finding, we call such a phenomenon "benign oscillation". Our theory towards demystifying such a phenomenon builds upon the feature learning perspective of deep learning. Specifically, we consider a feature-noise data generation model that consists of (i) weak features which have a small ell_2-norm and appear in each data point; (ii) strong features which have a larger ell_2-norm but only appear in a certain fraction of all data points; and (iii) noise. We prove that NNs trained by oscillating SGD with a large learning rate can effectively learn the weak features in the presence of those strong features. In contrast, NNs trained by SGD with a small learning rate can only learn the strong features but makes little progress in learning the weak features. Consequently, when it comes to the new testing data which consist of only weak features, the NN trained by oscillating SGD with a large learning rate could still make correct predictions consistently, while the NN trained by small learning rate SGD fails. Our theory sheds light on how large learning rate training benefits the generalization of NNs. Experimental results demonstrate our finding on "benign oscillation".

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Soft Actor Critic (SAC) algorithms show remarkable performance in complex simulated environments. A key element of SAC networks is entropy regularization, which prevents the SAC actor from optimizing against fine grained features, oftentimes transient, of the state-action value function. This results in better sample efficiency during early training. We take this idea one step further by artificially bandlimiting the target critic spatial resolution through the addition of a convolutional filter. We derive the closed form solution in the linear case and show that bandlimiting reduces the interdependency between the low and high frequency components of the state-action value approximation, allowing the critic to learn faster. In experiments, the bandlimited SAC outperformed the classic twin-critic SAC in a number of Gym environments, and displayed more stability in returns. We derive novel insights about SAC by adding a stochastic noise disturbance, a technique that is increasingly being used to learn robust policies that transfer well to the real world counterparts.

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.

The use of deep neural networks in reinforcement learning (RL) often suffers from performance degradation as model size increases. While soft mixtures of experts (SoftMoEs) have recently shown promise in mitigating this issue for online RL, the reasons behind their effectiveness remain largely unknown. In this work we provide an in-depth analysis identifying the key factors driving this performance gain. We discover the surprising result that tokenizing the encoder output, rather than the use of multiple experts, is what is behind the efficacy of SoftMoEs. Indeed, we demonstrate that even with an appropriately scaled single expert, we are able to maintain the performance gains, largely thanks to tokenization.

Distilling knowledge from a large teacher model to a lightweight one is a widely successful approach for generating compact, powerful models in the semi-supervised learning setting where a limited amount of labeled data is available. In large-scale applications, however, the teacher tends to provide a large number of incorrect soft-labels that impairs student performance. The sheer size of the teacher additionally constrains the number of soft-labels that can be queried due to prohibitive computational and/or financial costs. The difficulty in achieving simultaneous efficiency (i.e., minimizing soft-label queries) and robustness (i.e., avoiding student inaccuracies due to incorrect labels) hurts the widespread application of knowledge distillation to many modern tasks. In this paper, we present a parameter-free approach with provable guarantees to query the soft-labels of points that are simultaneously informative and correctly labeled by the teacher. At the core of our work lies a game-theoretic formulation that explicitly considers the inherent trade-off between the informativeness and correctness of input instances. We establish bounds on the expected performance of our approach that hold even in worst-case distillation instances. We present empirical evaluations on popular benchmarks that demonstrate the improved distillation performance enabled by our work relative to that of state-of-the-art active learning and active distillation methods.

In this paper, we focus on Whisper, a recent automatic speech recognition model trained with a massive 680k hour labeled speech corpus recorded in diverse conditions. We first show an interesting finding that while Whisper is very robust against real-world background sounds (e.g., music), its audio representation is actually not noise-invariant, but is instead highly correlated to non-speech sounds, indicating that Whisper recognizes speech conditioned on the noise type. With this finding, we build a unified audio tagging and speech recognition model Whisper-AT by freezing the backbone of Whisper, and training a lightweight audio tagging model on top of it. With <1% extra computational cost, Whisper-AT can recognize audio events, in addition to spoken text, in a single forward pass.

This paper investigates an under-explored challenge in large language models (LLMs): chain-of-thought prompting with noisy rationales, which include irrelevant or inaccurate reasoning thoughts within examples used for in-context learning. We construct NoRa dataset that is tailored to evaluate the robustness of reasoning in the presence of noisy rationales. Our findings on NoRa dataset reveal a prevalent vulnerability to such noise among current LLMs, with existing robust methods like self-correction and self-consistency showing limited efficacy. Notably, compared to prompting with clean rationales, base LLM drops by 1.4%-19.8% in accuracy with irrelevant thoughts and more drastically by 2.2%-40.4% with inaccurate thoughts. Addressing this challenge necessitates external supervision that should be accessible in practice. Here, we propose the method of contrastive denoising with noisy chain-of-thought (CD-CoT). It enhances LLMs' denoising-reasoning capabilities by contrasting noisy rationales with only one clean rationale, which can be the minimal requirement for denoising-purpose prompting. This method follows a principle of exploration and exploitation: (1) rephrasing and selecting rationales in the input space to achieve explicit denoising and (2) exploring diverse reasoning paths and voting on answers in the output space. Empirically, CD-CoT demonstrates an average improvement of 17.8% in accuracy over the base model and shows significantly stronger denoising capabilities than baseline methods. The source code is publicly available at: https://github.com/tmlr-group/NoisyRationales.

Real-world single image denoising is crucial and practical in computer vision. Bayesian inversions combined with score priors now have proven effective for single image denoising but are limited to white Gaussian noise. Moreover, applying existing score-based methods for real-world denoising requires not only the explicit train of score priors on the target domain but also the careful design of sampling procedures for posterior inference, which is complicated and impractical. To address these limitations, we propose a score priors-guided deep variational inference, namely ScoreDVI, for practical real-world denoising. By considering the deep variational image posterior with a Gaussian form, score priors are extracted based on easily accessible minimum MSE Non-i.i.d Gaussian denoisers and variational samples, which in turn facilitate optimizing the variational image posterior. Such a procedure adaptively applies cheap score priors to denoising. Additionally, we exploit a Non-i.i.d Gaussian mixture model and variational noise posterior to model the real-world noise. This scheme also enables the pixel-wise fusion of multiple image priors and variational image posteriors. Besides, we develop a noise-aware prior assignment strategy that dynamically adjusts the weight of image priors in the optimization. Our method outperforms other single image-based real-world denoising methods and achieves comparable performance to dataset-based unsupervised methods.

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with ell_1-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and--perhaps surprisingly--even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the ell_1-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

Prompt tuning is one of the successful approaches for parameter-efficient tuning of pre-trained language models. Despite being arguably the most parameter-efficient (tuned soft prompts constitute <0.1% of total parameters), it typically performs worse than other efficient tuning methods and is quite sensitive to hyper-parameters. In this work, we introduce Residual Prompt Tuning - a simple and efficient method that significantly improves the performance and stability of prompt tuning. We propose to reparameterize soft prompt embeddings using a shallow network with a residual connection. Our experiments show that Residual Prompt Tuning significantly outperforms prompt tuning on SuperGLUE benchmark. Notably, our method reaches +7 points improvement over prompt tuning with T5-Base and allows to reduce the prompt length by 10x without hurting performance. In addition, we show that our approach is robust to the choice of learning rate and prompt initialization, and is effective in few-shot settings.

In crowded settings, the human brain can focus on speech from a target speaker, given prior knowledge of how they sound. We introduce a novel intelligent hearable system that achieves this capability, enabling target speech hearing to ignore all interfering speech and noise, but the target speaker. A naive approach is to require a clean speech example to enroll the target speaker. This is however not well aligned with the hearable application domain since obtaining a clean example is challenging in real world scenarios, creating a unique user interface problem. We present the first enrollment interface where the wearer looks at the target speaker for a few seconds to capture a single, short, highly noisy, binaural example of the target speaker. This noisy example is used for enrollment and subsequent speech extraction in the presence of interfering speakers and noise. Our system achieves a signal quality improvement of 7.01 dB using less than 5 seconds of noisy enrollment audio and can process 8 ms of audio chunks in 6.24 ms on an embedded CPU. Our user studies demonstrate generalization to real-world static and mobile speakers in previously unseen indoor and outdoor multipath environments. Finally, our enrollment interface for noisy examples does not cause performance degradation compared to clean examples, while being convenient and user-friendly. Taking a step back, this paper takes an important step towards enhancing the human auditory perception with artificial intelligence. We provide code and data at: https://github.com/vb000/LookOnceToHear.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Understanding when the noise in stochastic gradient descent (SGD) affects generalization of deep neural networks remains a challenge, complicated by the fact that networks can operate in distinct training regimes. Here we study how the magnitude of this noise T affects performance as the size of the training set P and the scale of initialization alpha are varied. For gradient descent, alpha is a key parameter that controls if the network is `lazy'(alphagg1) or instead learns features (alphall1). For classification of MNIST and CIFAR10 images, our central results are: (i) obtaining phase diagrams for performance in the (alpha,T) plane. They show that SGD noise can be detrimental or instead useful depending on the training regime. Moreover, although increasing T or decreasing alpha both allow the net to escape the lazy regime, these changes can have opposite effects on performance. (ii) Most importantly, we find that the characteristic temperature T_c where the noise of SGD starts affecting the trained model (and eventually performance) is a power law of P. We relate this finding with the observation that key dynamical quantities, such as the total variation of weights during training, depend on both T and P as power laws. These results indicate that a key effect of SGD noise occurs late in training by affecting the stopping process whereby all data are fitted. Indeed, we argue that due to SGD noise, nets must develop a stronger `signal', i.e. larger informative weights, to fit the data, leading to a longer training time. A stronger signal and a longer training time are also required when the size of the training set P increases. We confirm these views in the perceptron model, where signal and noise can be precisely measured. Interestingly, exponents characterizing the effect of SGD depend on the density of data near the decision boundary, as we explain.

We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the generalization performance of existing methods is highly coupled with the quality of noisy labels. Therefore, we counter the problem from a novel and unified perspective: learning from the auxiliary clean labels. Specifically, we propose the Rotational-Decoupling Consistency Regularization (RDCR) framework that integrates the consistency-based methods with the self-supervised rotation task to learn noise-tolerant representations. The experiments show that RDCR achieves comparable or superior performance than the state-of-the-art methods under small noise, while outperforms the existing methods significantly when there is large noise.

As language models grow ever larger, so do their vocabularies. This has shifted the memory footprint of LLMs during training disproportionately to one single layer: the cross-entropy in the loss computation. Cross-entropy builds up a logit matrix with entries for each pair of input tokens and vocabulary items and, for small models, consumes an order of magnitude more memory than the rest of the LLM combined. We propose Cut Cross-Entropy (CCE), a method that computes the cross-entropy loss without materializing the logits for all tokens into global memory. Rather, CCE only computes the logit for the correct token and evaluates the log-sum-exp over all logits on the fly. We implement a custom kernel that performs the matrix multiplications and the log-sum-exp reduction over the vocabulary in flash memory, making global memory consumption for the cross-entropy computation negligible. This has a dramatic effect. Taking the Gemma 2 (2B) model as an example, CCE reduces the memory footprint of the loss computation from 24 GB to 1 MB, and the total training-time memory consumption of the classifier head from 28 GB to 1 GB. To improve the throughput of CCE, we leverage the inherent sparsity of softmax and propose to skip elements of the gradient computation that have a negligible (i.e., below numerical precision) contribution to the gradient. Experiments demonstrate that the dramatic reduction in memory consumption is accomplished without sacrificing training speed or convergence.

Dynamical generative models that produce samples through an iterative process, such as Flow Matching and denoising diffusion models, have seen widespread use, but there have not been many theoretically-sound methods for improving these models with reward fine-tuning. In this work, we cast reward fine-tuning as stochastic optimal control (SOC). Critically, we prove that a very specific memoryless noise schedule must be enforced during fine-tuning, in order to account for the dependency between the noise variable and the generated samples. We also propose a new algorithm named Adjoint Matching which outperforms existing SOC algorithms, by casting SOC problems as a regression problem. We find that our approach significantly improves over existing methods for reward fine-tuning, achieving better consistency, realism, and generalization to unseen human preference reward models, while retaining sample diversity.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show that the former allocates a model's capacity towards a subspace of the data explaining the observed variance--a subspace with uninformative features for the latter. For example, the supervised TinyImagenet task with images projected onto the top subspace explaining 90\% of the pixel variance can be solved with 45\% test accuracy. Using the bottom subspace instead, accounting for only 20\% of the pixel variance, reaches 55\% test accuracy. The features for perception being learned last explains the need for long training time, e.g., with Masked Autoencoders. Learning by denoising is a popular strategy to alleviate that misalignment. We prove that while some noise strategies such as masking are indeed beneficial, others such as additive Gaussian noise are not. Yet, even in the case of masking, we find that the benefits vary as a function of the mask's shape, ratio, and the considered dataset. While tuning the noise strategy without knowledge of the perception task seems challenging, we provide first clues on how to detect if a noise strategy is never beneficial regardless of the perception task.

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation t by striking a trade-off between a compression term I(x;t) and a prediction term I(y;t), where I(cdot;cdot) refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck.

Parameter Efficient Fine-Tuning (PEFT) methods have gained popularity and democratized the usage of Large Language Models (LLMs). Recent studies have shown that a small subset of weights significantly impacts performance. Based on this observation, we introduce a novel PEFT method, called Gaussian noise Injected Fine Tuning of Salient Weights (GIFT-SW). Our method updates only salient columns, while injecting Gaussian noise into non-salient ones. To identify these columns, we developeda generalized sensitivity metric that extends and unifies metrics from previous studies. Experiments with LLaMA models demonstrate that GIFT-SW outperforms full fine-tuning and modern PEFT methods under the same computational budget. Moreover, GIFT-SW offers practical advantages to recover performance of models subjected to mixed-precision quantization with keeping salient weights in full precision.

In an increasing number of domains it has been demonstrated that deep learning models can be trained using relatively large batch sizes without sacrificing data efficiency. However the limits of this massive data parallelism seem to differ from domain to domain, ranging from batches of tens of thousands in ImageNet to batches of millions in RL agents that play the game Dota 2. To our knowledge there is limited conceptual understanding of why these limits to batch size differ or how we might choose the correct batch size in a new domain. In this paper, we demonstrate that a simple and easy-to-measure statistic called the gradient noise scale predicts the largest useful batch size across many domains and applications, including a number of supervised learning datasets (MNIST, SVHN, CIFAR-10, ImageNet, Billion Word), reinforcement learning domains (Atari and Dota), and even generative model training (autoencoders on SVHN). We find that the noise scale increases as the loss decreases over a training run and depends on the model size primarily through improved model performance. Our empirically-motivated theory also describes the tradeoff between compute-efficiency and time-efficiency, and provides a rough model of the benefits of adaptive batch-size training.

We prove a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a representation r of the training data, and then fitting a simple (e.g., linear) classifier g to the labels. Specifically, we show that (under the assumptions described below) the generalization gap of such classifiers tends to zero if C(g) ll n, where C(g) is an appropriately-defined measure of the simple classifier g's complexity, and n is the number of training samples. We stress that our bound is independent of the complexity of the representation r. We do not make any structural or conditional-independence assumptions on the representation-learning task, which can use the same training dataset that is later used for classification. Rather, we assume that the training procedure satisfies certain natural noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely hold across many standard architectures. We show that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet, including SimCLR, AMDIM and MoCo.

For infinite action contextual bandits, smoothed regret and reduction to regression results in state-of-the-art online performance with computational cost independent of the action set: unfortunately, the resulting data exhaust does not have well-defined importance-weights. This frustrates the execution of downstream data science processes such as offline model selection. In this paper we describe an online algorithm with an equivalent smoothed regret guarantee, but which generates well-defined importance weights: in exchange, the online computational cost increases, but only to order smoothness (i.e., still independent of the action set). This removes a key obstacle to adoption of smoothed regret in production scenarios.

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

In this work, we build upon our previous publication and use diffusion-based generative models for speech enhancement. We present a detailed overview of the diffusion process that is based on a stochastic differential equation and delve into an extensive theoretical examination of its implications. Opposed to usual conditional generation tasks, we do not start the reverse process from pure Gaussian noise but from a mixture of noisy speech and Gaussian noise. This matches our forward process which moves from clean speech to noisy speech by including a drift term. We show that this procedure enables using only 30 diffusion steps to generate high-quality clean speech estimates. By adapting the network architecture, we are able to significantly improve the speech enhancement performance, indicating that the network, rather than the formalism, was the main limitation of our original approach. In an extensive cross-dataset evaluation, we show that the improved method can compete with recent discriminative models and achieves better generalization when evaluating on a different corpus than used for training. We complement the results with an instrumental evaluation using real-world noisy recordings and a listening experiment, in which our proposed method is rated best. Examining different sampler configurations for solving the reverse process allows us to balance the performance and computational speed of the proposed method. Moreover, we show that the proposed method is also suitable for dereverberation and thus not limited to additive background noise removal. Code and audio examples are available online, see https://github.com/sp-uhh/sgmse

Supervised learning can be viewed as distilling relevant information from input data into feature representations. This process becomes difficult when supervision is noisy as the distilled information might not be relevant. In fact, recent research shows that networks can easily overfit all labels including those that are corrupted, and hence can hardly generalize to clean datasets. In this paper, we focus on the problem of learning with noisy labels and introduce compression inductive bias to network architectures to alleviate this over-fitting problem. More precisely, we revisit one classical regularization named Dropout and its variant Nested Dropout. Dropout can serve as a compression constraint for its feature dropping mechanism, while Nested Dropout further learns ordered feature representations w.r.t. feature importance. Moreover, the trained models with compression regularization are further combined with Co-teaching for performance boost. Theoretically, we conduct bias-variance decomposition of the objective function under compression regularization. We analyze it for both single model and Co-teaching. This decomposition provides three insights: (i) it shows that over-fitting is indeed an issue for learning with noisy labels; (ii) through an information bottleneck formulation, it explains why the proposed feature compression helps in combating label noise; (iii) it gives explanations on the performance boost brought by incorporating compression regularization into Co-teaching. Experiments show that our simple approach can have comparable or even better performance than the state-of-the-art methods on benchmarks with real-world label noise including Clothing1M and ANIMAL-10N. Our implementation is available at https://yingyichen-cyy.github.io/CompressFeatNoisyLabels/.

Dictionary learning is a classic representation learning method that has been widely applied in signal processing and data analytics. In this paper, we investigate a family of ell_p-norm (p>2,p in N) maximization approaches for the complete dictionary learning problem from theoretical and algorithmic aspects. Specifically, we prove that the global maximizers of these formulations are very close to the true dictionary with high probability, even when Gaussian noise is present. Based on the generalized power method (GPM), an efficient algorithm is then developed for the ell_p-based formulations. We further show the efficacy of the developed algorithm: for the population GPM algorithm over the sphere constraint, it first quickly enters the neighborhood of a global maximizer, and then converges linearly in this region. Extensive experiments will demonstrate that the ell_p-based approaches enjoy a higher computational efficiency and better robustness than conventional approaches and p=3 performs the best.

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayes-optimal test error for classification while obtaining (nearly) zero-training error under the lazy training regime. For this purpose, we unify three interrelated concepts of overparameterization, benign overfitting, and the Lipschitz constant of DNNs. Our results indicate that interpolating with smoother functions leads to better generalization. Furthermore, we investigate the special case where interpolating smooth ground-truth functions is performed by DNNs under the Neural Tangent Kernel (NTK) regime for generalization. Our result demonstrates that the generalization error converges to a constant order that only depends on label noise and initialization noise, which theoretically verifies benign overfitting. Our analysis provides a tight lower bound on the normalized margin under non-smooth activation functions, as well as the minimum eigenvalue of NTK under high-dimensional settings, which has its own interest in learning theory.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

Methods with adaptive stepsizes, such as AdaGrad and Adam, are essential for training modern Deep Learning models, especially Large Language Models. Typically, the noise in the stochastic gradients is heavy-tailed for the later ones. Gradient clipping provably helps to achieve good high-probability convergence for such noises. However, despite the similarity between AdaGrad/Adam and Clip-SGD, the high-probability convergence of AdaGrad/Adam has not been studied in this case. In this work, we prove that AdaGrad (and its delayed version) can have provably bad high-probability convergence if the noise is heavy-tailed. To fix this issue, we propose a new version of AdaGrad called Clip-RAdaGradD (Clipped Reweighted AdaGrad with Delay) and prove its high-probability convergence bounds with polylogarithmic dependence on the confidence level for smooth convex/non-convex stochastic optimization with heavy-tailed noise. Our empirical evaluations, including NLP model fine-tuning, highlight the superiority of clipped versions of AdaGrad/Adam in handling the heavy-tailed noise.

Fine-tuning all the layers of a pre-trained neural language encoder (either using all the parameters or using parameter-efficient methods) is often the de-facto way of adapting it to a new task. We show evidence that for different downstream language tasks, fine-tuning only a subset of layers is sufficient to obtain performance that is close to and often better than fine-tuning all the layers in the language encoder. We propose an efficient metric based on the diagonal of the Fisher information matrix (FIM score), to select the candidate layers for selective fine-tuning. We show, empirically on GLUE and SuperGLUE tasks and across distinct language encoders, that this metric can effectively select layers leading to a strong downstream performance. Our work highlights that task-specific information corresponding to a given downstream task is often localized within a few layers, and tuning only those is sufficient for strong performance. Additionally, we demonstrate the robustness of the FIM score to rank layers in a manner that remains constant during the optimization process.

We propose a new strategy for applying large pre-trained language models to novel tasks when labeled training data is limited. Rather than apply the model in a typical zero-shot or few-shot fashion, we treat the model as the basis for labeling functions in a weak supervision framework. To create a classifier, we first prompt the model to answer multiple distinct queries about an example and define how the possible responses should be mapped to votes for labels and abstentions. We then denoise these noisy label sources using the Snorkel system and train an end classifier with the resulting training data. Our experimental evaluation shows that prompting large language models within a weak supervision framework can provide significant gains in accuracy. On the WRENCH weak supervision benchmark, this approach can significantly improve over zero-shot performance, an average 19.5% reduction in errors. We also find that this approach produces classifiers with comparable or superior accuracy to those trained from hand-engineered rules.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

Although there have been significant advances in the field of image restoration recently, the system complexity of the state-of-the-art (SOTA) methods is increasing as well, which may hinder the convenient analysis and comparison of methods. In this paper, we propose a simple baseline that exceeds the SOTA methods and is computationally efficient. To further simplify the baseline, we reveal that the nonlinear activation functions, e.g. Sigmoid, ReLU, GELU, Softmax, etc. are not necessary: they could be replaced by multiplication or removed. Thus, we derive a Nonlinear Activation Free Network, namely NAFNet, from the baseline. SOTA results are achieved on various challenging benchmarks, e.g. 33.69 dB PSNR on GoPro (for image deblurring), exceeding the previous SOTA 0.38 dB with only 8.4% of its computational costs; 40.30 dB PSNR on SIDD (for image denoising), exceeding the previous SOTA 0.28 dB with less than half of its computational costs. The code and the pre-trained models are released at https://github.com/megvii-research/NAFNet.

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.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Recently, convolutional networks have achieved remarkable development in remote sensing image Super-Resoltuion (SR) by minimizing the regression objectives, e.g., MSE loss. However, despite achieving impressive performance, these methods often suffer from poor visual quality with over-smooth issues. Generative adversarial networks have the potential to infer intricate details, but they are easy to collapse, resulting in undesirable artifacts. To mitigate these issues, in this paper, we first introduce Diffusion Probabilistic Model (DPM) for efficient remote sensing image SR, dubbed EDiffSR. EDiffSR is easy to train and maintains the merits of DPM in generating perceptual-pleasant images. Specifically, different from previous works using heavy UNet for noise prediction, we develop an Efficient Activation Network (EANet) to achieve favorable noise prediction performance by simplified channel attention and simple gate operation, which dramatically reduces the computational budget. Moreover, to introduce more valuable prior knowledge into the proposed EDiffSR, a practical Conditional Prior Enhancement Module (CPEM) is developed to help extract an enriched condition. Unlike most DPM-based SR models that directly generate conditions by amplifying LR images, the proposed CPEM helps to retain more informative cues for accurate SR. Extensive experiments on four remote sensing datasets demonstrate that EDiffSR can restore visual-pleasant images on simulated and real-world remote sensing images, both quantitatively and qualitatively. The code of EDiffSR will be available at https://github.com/XY-boy/EDiffSR

Crowdsourcing has emerged as an effective platform for labeling large amounts of data in a cost- and time-efficient manner. Most previous work has focused on designing an efficient algorithm to recover only the ground-truth labels of the data. In this paper, we consider multi-choice crowdsourcing tasks with the goal of recovering not only the ground truth, but also the most confusing answer and the confusion probability. The most confusing answer provides useful information about the task by revealing the most plausible answer other than the ground truth and how plausible it is. To theoretically analyze such scenarios, we propose a model in which there are the top two plausible answers for each task, distinguished from the rest of the choices. Task difficulty is quantified by the probability of confusion between the top two, and worker reliability is quantified by the probability of giving an answer among the top two. Under this model, we propose a two-stage inference algorithm to infer both the top two answers and the confusion probability. We show that our algorithm achieves the minimax optimal convergence rate. We conduct both synthetic and real data experiments and demonstrate that our algorithm outperforms other recent algorithms. We also show the applicability of our algorithms in inferring the difficulty of tasks and in training neural networks with top-two soft labels.

Deep learning methods have shown outstanding classification accuracy in medical imaging problems, which is largely attributed to the availability of large-scale datasets manually annotated with clean labels. However, given the high cost of such manual annotation, new medical imaging classification problems may need to rely on machine-generated noisy labels extracted from radiology reports. Indeed, many Chest X-ray (CXR) classifiers have already been modelled from datasets with noisy labels, but their training procedure is in general not robust to noisy-label samples, leading to sub-optimal models. Furthermore, CXR datasets are mostly multi-label, so current noisy-label learning methods designed for multi-class problems cannot be easily adapted. In this paper, we propose a new method designed for the noisy multi-label CXR learning, which detects and smoothly re-labels samples from the dataset, which is then used to train common multi-label classifiers. The proposed method optimises a bag of multi-label descriptors (BoMD) to promote their similarity with the semantic descriptors produced by BERT models from the multi-label image annotation. Our experiments on diverse noisy multi-label training sets and clean testing sets show that our model has state-of-the-art accuracy and robustness in many CXR multi-label classification benchmarks.

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of 1-bit quantization -- allow a high accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. Moreover, we empirically show by testing the performance of our methods on several machine learning tasks that our method compares favorably to other state of the art quantization methods in this context.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

In class incremental learning, neural networks typically suffer from catastrophic forgetting. We show that an MLP featuring a sparse activation function and an adaptive learning rate optimizer can compete with established regularization techniques in the Split-MNIST task. We highlight the effectiveness of the Adaptive SwisH (ASH) activation function in this context and introduce a novel variant, Hard Adaptive SwisH (Hard ASH) to further enhance the learning retention.

We investigate the expressive power of depth-2 bandlimited random neural networks. A random net is a neural network where the hidden layer parameters are frozen with random assignment, and only the output layer parameters are trained by loss minimization. Using random weights for a hidden layer is an effective method to avoid non-convex optimization in standard gradient descent learning. It has also been adopted in recent deep learning theories. Despite the well-known fact that a neural network is a universal approximator, in this study, we mathematically show that when hidden parameters are distributed in a bounded domain, the network may not achieve zero approximation error. In particular, we derive a new nontrivial approximation error lower bound. The proof utilizes the technique of ridgelet analysis, a harmonic analysis method designed for neural networks. This method is inspired by fundamental principles in classical signal processing, specifically the idea that signals with limited bandwidth may not always be able to perfectly recreate the original signal. We corroborate our theoretical results with various simulation studies, and generally, two main take-home messages are offered: (i) Not any distribution for selecting random weights is feasible to build a universal approximator; (ii) A suitable assignment of random weights exists but to some degree is associated with the complexity of the target function.

Adversarial examples, generated by carefully crafted perturbation, have attracted considerable attention in research fields. Recent works have argued that the existence of the robust and non-robust features is a primary cause of the adversarial examples, and investigated their internal interactions in the feature space. In this paper, we propose a way of explicitly distilling feature representation into the robust and non-robust features, using Information Bottleneck. Specifically, we inject noise variation to each feature unit and evaluate the information flow in the feature representation to dichotomize feature units either robust or non-robust, based on the noise variation magnitude. Through comprehensive experiments, we demonstrate that the distilled features are highly correlated with adversarial prediction, and they have human-perceptible semantic information by themselves. Furthermore, we present an attack mechanism intensifying the gradient of non-robust features that is directly related to the model prediction, and validate its effectiveness of breaking model robustness.

Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory to account for its occurrence in deep learning remains yet to be established. In this study, we revisit the phenomenon of double descent and demonstrate that its occurrence is strongly influenced by the presence of noisy data. Through conducting a comprehensive analysis of the feature space of learned representations, we unveil that double descent arises in imperfect models trained with noisy data. We argue that double descent is a consequence of the model first learning the noisy data until interpolation and then adding implicit regularization via over-parameterization acquiring therefore capability to separate the information from the noise.

Vision transformers (ViTs) have pushed the state-of-the-art for visual perception tasks. The self-attention mechanism underpinning the strength of ViTs has a quadratic complexity in both computation and memory usage. This motivates the development of approximating the self-attention at linear complexity. However, an in-depth analysis in this work reveals that existing methods are either theoretically flawed or empirically ineffective for visual recognition. We identify that their limitations are rooted in the inheritance of softmax-based self-attention during approximations, that is, normalizing the scaled dot-product between token feature vectors using the softmax function. As preserving the softmax operation challenges any subsequent linearization efforts. By this insight, a family of Softmax-Free Transformers (SOFT) are proposed. Specifically, a Gaussian kernel function is adopted to replace the dot-product similarity, enabling a full self-attention matrix to be approximated under low-rank matrix decomposition. For computational robustness, we estimate the Moore-Penrose inverse using an iterative Newton-Raphson method in the forward process only, while calculating its theoretical gradients only once in the backward process. To further expand applicability (e.g., dense prediction tasks), an efficient symmetric normalization technique is introduced. Extensive experiments on ImageNet, COCO, and ADE20K show that our SOFT significantly improves the computational efficiency of existing ViT variants. With linear complexity, much longer token sequences are permitted by SOFT, resulting in superior trade-off between accuracy and complexity. Code and models are available at https://github.com/fudan-zvg/SOFT.

Machine learning models are vulnerable to adversarial perturbations, and a thought-provoking paper by Bubeck and Sellke has analyzed this phenomenon through the lens of over-parameterization: interpolating smoothly the data requires significantly more parameters than simply memorizing it. However, this "universal" law provides only a necessary condition for robustness, and it is unable to discriminate between models. In this paper, we address these gaps by focusing on empirical risk minimization in two prototypical settings, namely, random features and the neural tangent kernel (NTK). We prove that, for random features, the model is not robust for any degree of over-parameterization, even when the necessary condition coming from the universal law of robustness is satisfied. In contrast, for even activations, the NTK model meets the universal lower bound, and it is robust as soon as the necessary condition on over-parameterization is fulfilled. This also addresses a conjecture in prior work by Bubeck, Li and Nagaraj. Our analysis decouples the effect of the kernel of the model from an "interaction matrix", which describes the interaction with the test data and captures the effect of the activation. Our theoretical results are corroborated by numerical evidence on both synthetic and standard datasets (MNIST, CIFAR-10).

Traditional methods for learning with the presence of noisy labels have successfully handled datasets with artificially injected noise but still fall short of adequately handling real-world noise. With the increasing use of meta-learning in the diverse fields of machine learning, researchers leveraged auxiliary small clean datasets to meta-correct the training labels. Nonetheless, existing meta-label correction approaches are not fully exploiting their potential. In this study, we propose an Enhanced Meta Label Correction approach abbreviated as EMLC for the learning with noisy labels (LNL) problem. We re-examine the meta-learning process and introduce faster and more accurate meta-gradient derivations. We propose a novel teacher architecture tailored explicitly to the LNL problem, equipped with novel training objectives. EMLC outperforms prior approaches and achieves state-of-the-art results in all standard benchmarks. Notably, EMLC enhances the previous art on the noisy real-world dataset Clothing1M by 1.52% while requiring times 0.5 the time per epoch and with much faster convergence of the meta-objective when compared to the baseline approach.

Adversarial examples cause neural networks to produce incorrect outputs with high confidence. Although adversarial training is one of the most effective forms of defense against adversarial examples, unfortunately, a large gap exists between test accuracy and training accuracy in adversarial training. In this paper, we identify Adversarial Feature Overfitting (AFO), which may cause poor adversarially robust generalization, and we show that adversarial training can overshoot the optimal point in terms of robust generalization, leading to AFO in our simple Gaussian model. Considering these theoretical results, we present soft labeling as a solution to the AFO problem. Furthermore, we propose Adversarial Vertex mixup (AVmixup), a soft-labeled data augmentation approach for improving adversarially robust generalization. We complement our theoretical analysis with experiments on CIFAR10, CIFAR100, SVHN, and Tiny ImageNet, and show that AVmixup significantly improves the robust generalization performance and that it reduces the trade-off between standard accuracy and adversarial robustness.

The vulnerability of deep neural networks to adversarial samples has been a major impediment to their broad applications, despite their success in various fields. Recently, some works suggested that adversarially-trained models emphasize the importance of low-frequency information to achieve higher robustness. While several attempts have been made to leverage this frequency characteristic, they have all faced the issue that applying low-pass filters directly to input images leads to irreversible loss of discriminative information and poor generalizability to datasets with distinct frequency features. This paper presents a plug-and-play module called the Frequency Preference Control Module that adaptively reconfigures the low- and high-frequency components of intermediate feature representations, providing better utilization of frequency in robust learning. Empirical studies show that our proposed module can be easily incorporated into any adversarial training framework, further improving model robustness across different architectures and datasets. Additionally, experiments were conducted to examine how the frequency bias of robust models impacts the adversarial training process and its final robustness, revealing interesting insights.

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an inference network on simulated data, which can subsequently be used to rapidly perform inference (i.e., to return estimates of posterior distributions) for new observations. This approach has been applied to many real-world models in the sciences and engineering, but it is unclear how robust the approach is to adversarial perturbations in the observed data. Here, we study the adversarial robustness of amortized Bayesian inference, focusing on simulation-based estimation of multi-dimensional posterior distributions. We show that almost unrecognizable, targeted perturbations of the observations can lead to drastic changes in the predicted posterior and highly unrealistic posterior predictive samples, across several benchmark tasks and a real-world example from neuroscience. We propose a computationally efficient regularization scheme based on penalizing the Fisher information of the conditional density estimator, and show how it improves the adversarial robustness of amortized Bayesian inference.

Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and developing different practical strategies to enforce certain Lipschitz properties, we aim to thoroughly examine and characterise the Lipschitz behaviour of Neural Networks. Thus, we carry out an empirical investigation in a range of different settings (namely, architectures, datasets, label noise, and more) by exhausting the limits of the simplest and the most general lower and upper bounds. As a highlight of this investigation, we showcase a remarkable fidelity of the lower Lipschitz bound, identify a striking Double Descent trend in both upper and lower bounds to the Lipschitz and explain the intriguing effects of label noise on function smoothness and generalisation.

While prompt tuning approaches have achieved competitive performance with high efficiency, we observe that they invariably employ the same initialization process, wherein the soft prompt is either randomly initialized or derived from an existing embedding vocabulary. In contrast to these conventional methods, this study aims to investigate an alternative way to derive soft prompt. Our empirical studies show that the soft prompt typically exhibits a low intrinsic rank characteristic. With such observations, we propose decomposed prompt tuning, a novel approach that utilizes low-rank matrices to initialize the soft prompt. Through the low-rank reparameterization, our method significantly reduces the number of trainable parameters while maintaining effectiveness. Experimental results on the SuperGLUE benchmark in both high-resource and low-resource scenarios demonstrate the effectiveness of the proposed method.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

Denoising Score Matching estimates the score of a noised version of a target distribution by minimizing a regression loss and is widely used to train the popular class of Denoising Diffusion Models. A well known limitation of Denoising Score Matching, however, is that it yields poor estimates of the score at low noise levels. This issue is particularly unfavourable for problems in the physical sciences and for Monte Carlo sampling tasks for which the score of the clean original target is known. Intuitively, estimating the score of a slightly noised version of the target should be a simple task in such cases. In this paper, we address this shortcoming and show that it is indeed possible to leverage knowledge of the target score. We present a Target Score Identity and corresponding Target Score Matching regression loss which allows us to obtain score estimates admitting favourable properties at low noise levels.

The high computational costs of large language models (LLMs) have led to a flurry of research on LLM compression, via methods such as quantization, sparsification, or structured pruning. A new frontier in this area is given by dynamic, non-uniform compression methods, which adjust the compression levels (e.g., sparsity) per-block or even per-layer in order to minimize accuracy loss, while guaranteeing a global compression threshold. Yet, current methods rely on heuristics for identifying the "importance" of a given layer towards the loss, based on assumptions such as error monotonicity, i.e. that the end-to-end model compression error is proportional to the sum of layer-wise errors. In this paper, we revisit this area, and propose a new and general approach for dynamic compression that is provably optimal in a given input range. We begin from the motivating observation that, in general, error monotonicity does not hold for LLMs: compressed models with lower sum of per-layer errors can perform worse than models with higher error sums. To address this, we propose a new general evolutionary framework for dynamic LLM compression called EvoPress, which has provable convergence, and low sample and evaluation complexity. We show that these theoretical guarantees lead to highly competitive practical performance for dynamic compression of Llama, Mistral and Phi models. Via EvoPress, we set new state-of-the-art results across all compression approaches: structural pruning (block/layer dropping), unstructured sparsity, as well as quantization with dynamic bitwidths. Our code is available at https://github.com/IST-DASLab/EvoPress.

There are two widely known issues with properly training Recurrent Neural Networks, the vanishing and the exploding gradient problems detailed in Bengio et al. (1994). In this paper we attempt to improve the understanding of the underlying issues by exploring these problems from an analytical, a geometric and a dynamical systems perspective. Our analysis is used to justify a simple yet effective solution. We propose a gradient norm clipping strategy to deal with exploding gradients and a soft constraint for the vanishing gradients problem. We validate empirically our hypothesis and proposed solutions in the experimental section.

There are several applications of stochastic optimization where one can benefit from a robust estimate of the gradient. For example, domains such as distributed learning with corrupted nodes, the presence of large outliers in the training data, learning under privacy constraints, or even heavy-tailed noise due to the dynamics of the algorithm itself. Here we study SGD with robust gradient estimators based on estimating the median. We first consider computing the median gradient across samples, and show that the resulting method can converge even under heavy-tailed, state-dependent noise. We then derive iterative methods based on the stochastic proximal point method for computing the geometric median and generalizations thereof. Finally we propose an algorithm estimating the median gradient across iterations, and find that several well known methods - in particular different forms of clipping - are particular cases of this framework.

Diffusion models have emerged as the de facto choice for generating visual signals. However, training a single model to predict noise across various levels poses significant challenges, necessitating numerous iterations and incurring significant computational costs. Various approaches, such as loss weighting strategy design and architectural refinements, have been introduced to expedite convergence. In this study, we propose a novel approach to design the noise schedule for enhancing the training of diffusion models. Our key insight is that the importance sampling of the logarithm of the Signal-to-Noise ratio (logSNR), theoretically equivalent to a modified noise schedule, is particularly beneficial for training efficiency when increasing the sample frequency around log SNR=0. We empirically demonstrate the superiority of our noise schedule over the standard cosine schedule. Furthermore, we highlight the advantages of our noise schedule design on the ImageNet benchmark, showing that the designed schedule consistently benefits different prediction targets.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size -- on certain non-convex function classes -- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

While implicit feedback is foundational to modern recommender systems, factors such as human error, uncertainty, and ambiguity in user behavior inevitably introduce significant noise into this feedback, adversely affecting the accuracy and robustness of recommendations. To address this issue, existing methods typically aim to reduce the training weight of noisy feedback or discard it entirely, based on the observation that noisy interactions often exhibit higher losses in the overall loss distribution. However, we identify two key issues: (1) there is a significant overlap between normal and noisy interactions in the overall loss distribution, and (2) this overlap becomes even more pronounced when transitioning from pointwise loss functions (e.g., BCE loss) to pairwise loss functions (e.g., BPR loss). This overlap leads traditional methods to misclassify noisy interactions as normal, and vice versa. To tackle these challenges, we further investigate the loss overlap and find that for a given user, there is a clear distinction between normal and noisy interactions in the user's personal loss distribution. Based on this insight, we propose a resampling strategy to Denoise using the user's Personal Loss distribution, named PLD, which reduces the probability of noisy interactions being optimized. Specifically, during each optimization iteration, we create a candidate item pool for each user and resample the items from this pool based on the user's personal loss distribution, prioritizing normal interactions. Additionally, we conduct a theoretical analysis to validate PLD's effectiveness and suggest ways to further enhance its performance. Extensive experiments conducted on three datasets with varying noise ratios demonstrate PLD's efficacy and robustness.

Deep Image Prior (DIP) shows that some network architectures naturally bias towards smooth images and resist noises, a phenomenon known as spectral bias. Image denoising is an immediate application of this property. Although DIP has removed the requirement of large training sets, it still presents two practical challenges for denoising: architectural design and noise-fitting, which are often intertwined. Existing methods mostly handcraft or search for the architecture from a large design space, due to the lack of understanding on how the architectural choice corresponds to the image. In this study, we analyze from a frequency perspective to demonstrate that the unlearnt upsampling is the main driving force behind the denoising phenomenon in DIP. This finding then leads to strategies for estimating a suitable architecture for every image without a laborious search. Extensive experiments show that the estimated architectures denoise and preserve the textural details better than current methods with up to 95% fewer parameters. The under-parameterized nature also makes them especially robust to a higher level of noise.

Label smoothing (LS) is a popular regularisation method for training deep neural network classifiers due to its effectiveness in improving test accuracy and its simplicity in implementation. "Hard" one-hot labels are "smoothed" by uniformly distributing probability mass to other classes, reducing overfitting. In this work, we reveal that LS negatively affects selective classification (SC) - where the aim is to reject misclassifications using a model's predictive uncertainty. We first demonstrate empirically across a range of tasks and architectures that LS leads to a consistent degradation in SC. We then explain this by analysing logit-level gradients, showing that LS exacerbates overconfidence and underconfidence by regularising the max logit more when the probability of error is low, and less when the probability of error is high. This elucidates previously reported experimental results where strong classifiers underperform in SC. We then demonstrate the empirical effectiveness of logit normalisation for recovering lost SC performance caused by LS. Furthermore, based on our gradient analysis, we explain why such normalisation is effective. We will release our code shortly.

The goal of voice conversion is to transform source speech into a target voice, keeping the content unchanged. In this paper, we focus on self-supervised representation learning for voice conversion. Specifically, we compare discrete and soft speech units as input features. We find that discrete representations effectively remove speaker information but discard some linguistic content - leading to mispronunciations. As a solution, we propose soft speech units. To learn soft units, we predict a distribution over discrete speech units. By modeling uncertainty, soft units capture more content information, improving the intelligibility and naturalness of converted speech. Samples available at https://ubisoft-laforge.github.io/speech/soft-vc/. Code available at https://github.com/bshall/soft-vc/.

This work aims to advance sound event detection (SED) research by presenting a new large language model (LLM)-powered dataset namely wild domestic environment sound event detection (WildDESED). It is crafted as an extension to the original DESED dataset to reflect diverse acoustic variability and complex noises in home settings. We leveraged LLMs to generate eight different domestic scenarios based on target sound categories of the DESED dataset. Then we enriched the scenarios with a carefully tailored mixture of noises selected from AudioSet and ensured no overlap with target sound. We consider widely popular convolutional neural recurrent network to study WildDESED dataset, which depicts its challenging nature. We then apply curriculum learning by gradually increasing noise complexity to enhance the model's generalization capabilities across various noise levels. Our results with this approach show improvements within the noisy environment, validating the effectiveness on the WildDESED dataset promoting noise-robust SED advancements.

Mixture of experts (MoE) has a well-principled finite mixture model construction for prediction, allowing the gating network (mixture weights) to learn from the predictors (explanatory variables) together with the experts' network (mixture component densities). We investigate the estimation properties of MoEs in a high-dimensional setting, where the number of predictors is much larger than the sample size, for which the literature lacks computational and especially theoretical results. We consider the class of finite MoE models with softmax gating functions and Gaussian regression experts, and focus on the theoretical properties of their l_1-regularized estimation via the Lasso. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures an l_1-oracle inequality is satisfied by the Lasso estimator according to the Kullback--Leibler loss. We further state an l_1-ball oracle inequality for the l_1-penalized maximum likelihood estimator from the model selection.

In this paper, we present an embarrassingly simple yet effective solution to a seemingly impossible mission, low-light image enhancement (LLIE) without access to any task-related data. The proposed solution, Noise SElf-Regression (NoiSER), simply learns a convolutional neural network equipped with a instance-normalization layer by taking a random noise image, N(0,sigma^2) for each pixel, as both input and output for each training pair, and then the low-light image is fed to the learned network for predicting the normal-light image. Technically, an intuitive explanation for its effectiveness is as follows: 1) the self-regression reconstructs the contrast between adjacent pixels of the input image, 2) the instance-normalization layers may naturally remediate the overall magnitude/lighting of the input image, and 3) the N(0,sigma^2) assumption for each pixel enforces the output image to follow the well-known gray-world hypothesis Gary-world_Hypothesis when the image size is big enough, namely, the averages of three RGB components of an image converge to the same value. Compared to existing SOTA LLIE methods with access to different task-related data, NoiSER is surprisingly highly competitive in enhancement quality, yet with a much smaller model size, and much lower training and inference cost. With only sim 1K parameters, NoiSER realizes about 1 minute for training and 1.2 ms for inference with 600x400 resolution on RTX 2080 Ti. As a bonus, NoiSER possesses automated over-exposure suppression ability and shows excellent performance on over-exposed photos.

Robustness and compactness are two essential attributes of deep learning models that are deployed in the real world. The goals of robustness and compactness may seem to be at odds, since robustness requires generalization across domains, while the process of compression exploits specificity in one domain. We introduce Adaptive Sharpness-Aware Pruning (AdaSAP), which unifies these goals through the lens of network sharpness. The AdaSAP method produces sparse networks that are robust to input variations which are unseen at training time. We achieve this by strategically incorporating weight perturbations in order to optimize the loss landscape. This allows the model to be both primed for pruning and regularized for improved robustness. AdaSAP improves the robust accuracy of pruned models on image classification by up to +6% on ImageNet C and +4% on ImageNet V2, and on object detection by +4% on a corrupted Pascal VOC dataset, over a wide range of compression ratios, pruning criteria, and network architectures, outperforming recent pruning art by large margins.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability eta(x)=P(Y=1mid X=x), we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of 2eta(x)-1 and apply the method to real datasets.

It is typically understood that the training of modern neural networks is a process of fitting the probability distribution of desired output. However, recent paradoxical observations in a number of language generation tasks let one wonder if this canonical probability-based explanation can really account for the empirical success of deep learning. To resolve this issue, we propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function that encodes the preference revealed in training data. In this perspective, training of the neural network corresponds to a utility learning process. Specifically, we show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation (MLE) can be seen as an iteration process that optimizes the neural network toward an optimal utility function. This utility-based interpretation can explain several otherwise-paradoxical observations about the neural networks thus trained. Moreover, our utility-based theory also entails an equation that can transform the learned utility values back to a new kind of probability estimation with which probability-compatible decision rules enjoy dramatic (double-digits) performance improvements. These evidences collectively reveal a phenomenon of utility-probability duality in terms of what modern neural networks are (truly) modeling: We thought they are one thing (probabilities), until the unexplainable showed up; changing mindset and treating them as another thing (utility values) largely reconcile the theory, despite remaining subtleties regarding its original (probabilistic) identity.

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.

Deep learning in the presence of noisy annotations has been studied extensively in classification, but much less in segmentation tasks. In this work, we study the learning dynamics of deep segmentation networks trained on inaccurately-annotated data. We discover a phenomenon that has been previously reported in the context of classification: the networks tend to first fit the clean pixel-level labels during an "early-learning" phase, before eventually memorizing the false annotations. However, in contrast to classification, memorization in segmentation does not arise simultaneously for all semantic categories. Inspired by these findings, we propose a new method for segmentation from noisy annotations with two key elements. First, we detect the beginning of the memorization phase separately for each category during training. This allows us to adaptively correct the noisy annotations in order to exploit early learning. Second, we incorporate a regularization term that enforces consistency across scales to boost robustness against annotation noise. Our method outperforms standard approaches on a medical-imaging segmentation task where noises are synthesized to mimic human annotation errors. It also provides robustness to realistic noisy annotations present in weakly-supervised semantic segmentation, achieving state-of-the-art results on PASCAL VOC 2012. Code is available at https://github.com/Kangningthu/ADELE

Removing background noise from speech audio has been the subject of considerable effort, especially in recent years due to the rise of virtual communication and amateur recordings. Yet background noise is not the only unpleasant disturbance that can prevent intelligibility: reverb, clipping, codec artifacts, problematic equalization, limited bandwidth, or inconsistent loudness are equally disturbing and ubiquitous. In this work, we propose to consider the task of speech enhancement as a holistic endeavor, and present a universal speech enhancement system that tackles 55 different distortions at the same time. Our approach consists of a generative model that employs score-based diffusion, together with a multi-resolution conditioning network that performs enhancement with mixture density networks. We show that this approach significantly outperforms the state of the art in a subjective test performed by expert listeners. We also show that it achieves competitive objective scores with just 4-8 diffusion steps, despite not considering any particular strategy for fast sampling. We hope that both our methodology and technical contributions encourage researchers and practitioners to adopt a universal approach to speech enhancement, possibly framing it as a generative task.

Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However how to design an efficient classifier with an associated certified radius? Randomized smoothing provides a promising framework by relying on noise injection into the inputs to obtain a smoothed and robust classifier. In this paper, we first show that the variance introduced by the Monte-Carlo sampling in the randomized smoothing procedure estimate closely interacts with two other important properties of the classifier, i.e. its Lipschitz constant and margin. More precisely, our work emphasizes the dual impact of the Lipschitz constant of the base classifier, on both the smoothed classifier and the empirical variance. To increase the certified robust radius, we introduce a different way to convert logits to probability vectors for the base classifier to leverage the variance-margin trade-off. We leverage the use of Bernstein's concentration inequality along with enhanced Lipschitz bounds for randomized smoothing. Experimental results show a significant improvement in certified accuracy compared to current state-of-the-art methods. Our novel certification procedure allows us to use pre-trained models with randomized smoothing, effectively improving the current certification radius in a zero-shot manner.

In standard adversarial training, models are optimized to fit one-hot labels within allowable adversarial perturbation budgets. However, the ignorance of underlying distribution shifts brought by perturbations causes the problem of robust overfitting. To address this issue and enhance adversarial robustness, we analyze the characteristics of robust models and identify that robust models tend to produce smoother and well-calibrated outputs. Based on the observation, we propose a simple yet effective method, Annealing Self-Distillation Rectification (ADR), which generates soft labels as a better guidance mechanism that accurately reflects the distribution shift under attack during adversarial training. By utilizing ADR, we can obtain rectified distributions that significantly improve model robustness without the need for pre-trained models or extensive extra computation. Moreover, our method facilitates seamless plug-and-play integration with other adversarial training techniques by replacing the hard labels in their objectives. We demonstrate the efficacy of ADR through extensive experiments and strong performances across datasets.

We empirically study the effect of noise scheduling strategies for denoising diffusion generative models. There are three findings: (1) the noise scheduling is crucial for the performance, and the optimal one depends on the task (e.g., image sizes), (2) when increasing the image size, the optimal noise scheduling shifts towards a noisier one (due to increased redundancy in pixels), and (3) simply scaling the input data by a factor of b while keeping the noise schedule function fixed (equivalent to shifting the logSNR by log b) is a good strategy across image sizes. This simple recipe, when combined with recently proposed Recurrent Interface Network (RIN), yields state-of-the-art pixel-based diffusion models for high-resolution images on ImageNet, enabling single-stage, end-to-end generation of diverse and high-fidelity images at 1024times1024 resolution (without upsampling/cascades).

Recent works have revealed that infinitely-wide feed-forward or recurrent neural networks of any architecture correspond to Gaussian processes referred to as Neural Network Gaussian Processes (NNGPs). While these works have extended the class of neural networks converging to Gaussian processes significantly, however, there has been little focus on broadening the class of stochastic processes that such neural networks converge to. In this work, inspired by the scale mixture of Gaussian random variables, we propose the scale mixture of NNGPs for which we introduce a prior distribution on the scale of the last-layer parameters. We show that simply introducing a scale prior on the last-layer parameters can turn infinitely-wide neural networks of any architecture into a richer class of stochastic processes. With certain scale priors, we obtain heavy-tailed stochastic processes, and in the case of inverse gamma priors, we recover Student's t processes. We further analyze the distributions of the neural networks initialized with our prior setting and trained with gradient descents and obtain similar results as for NNGPs. We present a practical posterior-inference algorithm for the scale mixture of NNGPs and empirically demonstrate its usefulness on regression and classification tasks. In particular, we show that in both tasks, the heavy-tailed stochastic processes obtained from our framework are robust to out-of-distribution data.

N:M Structured sparsity has garnered significant interest as a result of relatively modest overhead and improved efficiency. Additionally, this form of sparsity holds considerable appeal for reducing the memory footprint owing to their modest representation overhead. There have been efforts to develop training recipes for N:M structured sparsity, they primarily focus on low-sparsity regions (sim50\%). Nonetheless, performance of models trained using these approaches tends to decline when confronted with high-sparsity regions (>80\%). In this work, we study the effectiveness of existing sparse training recipes at high-sparsity regions and argue that these methods fail to sustain the model quality on par with low-sparsity regions. We demonstrate that the significant factor contributing to this disparity is the presence of elevated levels of induced noise in the gradient magnitudes. To mitigate this undesirable effect, we employ decay mechanisms to progressively restrict the flow of gradients towards pruned elements. Our approach improves the model quality by up to 2% and 5% in vision and language models at high sparsity regime, respectively. We also evaluate the trade-off between model accuracy and training compute cost in terms of FLOPs. At iso-training FLOPs, our method yields better performance compared to conventional sparse training recipes, exhibiting an accuracy improvement of up to 2%. The source code is available at https://github.com/abhibambhaniya/progressive_gradient_flow_nm_sparsity.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

We study the SAM (Sharpness-Aware Minimization) optimizer which has recently attracted a lot of interest due to its increased performance over more classical variants of stochastic gradient descent. Our main contribution is the derivation of continuous-time models (in the form of SDEs) for SAM and two of its variants, both for the full-batch and mini-batch settings. We demonstrate that these SDEs are rigorous approximations of the real discrete-time algorithms (in a weak sense, scaling linearly with the learning rate). Using these models, we then offer an explanation of why SAM prefers flat minima over sharp ones~--~by showing that it minimizes an implicitly regularized loss with a Hessian-dependent noise structure. Finally, we prove that SAM is attracted to saddle points under some realistic conditions. Our theoretical results are supported by detailed experiments.

The generalization and learning speed of a multi-class neural network can often be significantly improved by using soft targets that are a weighted average of the hard targets and the uniform distribution over labels. Smoothing the labels in this way prevents the network from becoming over-confident and label smoothing has been used in many state-of-the-art models, including image classification, language translation and speech recognition. Despite its widespread use, label smoothing is still poorly understood. Here we show empirically that in addition to improving generalization, label smoothing improves model calibration which can significantly improve beam-search. However, we also observe that if a teacher network is trained with label smoothing, knowledge distillation into a student network is much less effective. To explain these observations, we visualize how label smoothing changes the representations learned by the penultimate layer of the network. We show that label smoothing encourages the representations of training examples from the same class to group in tight clusters. This results in loss of information in the logits about resemblances between instances of different classes, which is necessary for distillation, but does not hurt generalization or calibration of the model's predictions.

While instruction-tuned language models have demonstrated impressive zero-shot generalization, these models often struggle to generate accurate responses when faced with instructions that fall outside their training set. This paper presents Instructive Decoding (ID), a simple yet effective approach that augments the efficacy of instruction-tuned models. Specifically, ID adjusts the logits for next-token prediction in a contrastive manner, utilizing predictions generated from a manipulated version of the original instruction, referred to as a noisy instruction. This noisy instruction aims to elicit responses that could diverge from the intended instruction yet remain plausible. We conduct experiments across a spectrum of such noisy instructions, ranging from those that insert semantic noise via random words to others like 'opposite' that elicit the deviated responses. Our approach achieves considerable performance gains across various instruction-tuned models and tasks without necessitating any additional parameter updates. Notably, utilizing 'opposite' as the noisy instruction in ID, which exhibits the maximum divergence from the original instruction, consistently produces the most significant performance gains across multiple models and tasks.