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0 |
Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent
|
https://openreview.net/forum?id=2GmXJnyNM4
|
[
"Santhosh Karnik",
"Anna Veselovska",
"Mark Iwen",
"Felix Krahmer"
] |
Oral
|
We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, this phenomenon has been studied in a number of works. A particular challenge has been to design universal initialization strategies which provably lead to implicit regularization in gradient-descent methods. At the same time, it has been argued by Cohen et. al. 2016 that more general classes of neural networks can be captured by considering tensor factorizations. However, in the tensor case, implicit regularization has only been rigorously established for gradient flow or in the lazy training regime. In this paper, we prove the first tensor result of its kind for gradient descent rather than gradient flow. We focus on the tubal tensor product and the associated notion of low tubal rank, encouraged by the relevance of this model for image data. We establish that gradient descent in an overparametrized tensor factorization model with a small random initialization exhibits an implicit bias towards solutions of low tubal rank. Our theoretical findings are illustrated in an extensive set of numerical simulations show-casing the dynamics predicted by our theory as well as the crucial role of using a small random initialization.
|
overparameterization, implicit regularization, tensor factorization
|
We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime.
| 16,047 |
2410.16247
|
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] |
https://github.com/AnnaVeselovskaUA/tubal-tensor-implicit-reg-GD
|
1 |
Algorithm Development in Neural Networks: Insights from the Streaming Parity Task
|
https://openreview.net/forum?id=3go0lhfxd0
|
[
"Loek van Rossem",
"Andrew M Saxe"
] |
Oral
|
Even when massively overparameterized, deep neural networks show a remarkable ability to generalize. Research on this phenomenon has focused on generalization within distribution, via smooth interpolation. Yet in some settings neural networks also learn to extrapolate to data far beyond the bounds of the original training set, sometimes even allowing for infinite generalization, implying that an algorithm capable of solving the task has been learned. Here we undertake a case study of the learning dynamics of recurrent neural networks trained on the streaming parity task in order to develop an effective theory of algorithm development. The streaming parity task is a simple but nonlinear task defined on sequences up to arbitrary length. We show that, with sufficient finite training experience, RNNs exhibit a phase transition to perfect infinite generalization. Using an effective theory for the representational dynamics, we find an implicit representational merger effect which can be interpreted as the construction of a finite automaton that reproduces the task. Overall, our results disclose one mechanism by which neural networks can generalize infinitely from finite training experience.
|
Out-of-distribution generalization, Algorithm discovery, Deep learning theory, Mechanistic Interpretability
|
We explain in a simple setting how out-of-distribution generalization can occur.
| 16,013 |
2507.09897
|
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] | null |
2 |
Orthogonal Subspace Decomposition for Generalizable AI-Generated Image Detection
|
https://openreview.net/forum?id=GFpjO8S8Po
|
[
"Zhiyuan Yan",
"Jiangming Wang",
"Peng Jin",
"Ke-Yue Zhang",
"Chengchun Liu",
"Shen Chen",
"Taiping Yao",
"Shouhong Ding",
"Baoyuan Wu",
"Li Yuan"
] |
Oral
|
Detecting AI-generated images (AIGIs), such as natural images or face images, has become increasingly important yet challenging. In this paper, we start from a new perspective to excavate the reason behind the failure generalization in AIGI detection, named the asymmetry phenomenon, where a naively trained detector tends to favor overfitting to the limited and monotonous fake patterns, causing the feature space to become highly constrained and low-ranked, which is proved seriously limiting the expressivity and generalization. One potential remedy is incorporating the pre-trained knowledge within the vision foundation models (higher-ranked) to expand the feature space, alleviating the model's overfitting to fake. To this end, we employ Singular Value Decomposition (SVD) to decompose the original feature space into two orthogonal subspaces. By freezing the principal components and adapting only the remained components, we preserve the pre-trained knowledge while learning fake patterns. Compared to existing full-parameters and LoRA-based tuning methods, we explicitly ensure orthogonality, enabling the higher rank of the whole feature space, effectively minimizing overfitting and enhancing generalization. We finally identify a crucial insight: our method implicitly learns a vital prior that fakes are actually derived from the real, indicating a hierarchical relationship rather than independence. Modeling this prior, we believe, is essential for achieving superior generalization. Our codes are publicly available at https://github.com/YZY-stack/Effort-AIGI-Detection.
|
AI-Generated Image Detection, Face Forgery Detection, Deepfake Detection, Media Forensics
|
We introduce a novel approach via orthogonal subspace decomposition for generalizing AI-generated images detection.
| 15,222 |
2411.15633
|
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] |
https://github.com/YZY-stack/Effort-AIGI-Detection
|
3 |
Accelerating LLM Inference with Lossless Speculative Decoding Algorithms for Heterogeneous Vocabularies
|
https://openreview.net/forum?id=vQubr1uBUw
|
[
"Nadav Timor",
"Jonathan Mamou",
"Daniel Korat",
"Moshe Berchansky",
"Gaurav Jain",
"Oren Pereg",
"Moshe Wasserblat",
"David Harel"
] |
Oral
|
Accelerating the inference of large language models (LLMs) is a critical challenge in generative AI. Speculative decoding (SD) methods offer substantial efficiency gains by generating multiple tokens using a single target forward pass. However, existing SD approaches require the drafter and target models to share the same vocabulary, thus limiting the pool of possible drafters, often necessitating the training of a drafter from scratch. We present three new SD methods that remove this shared-vocabulary constraint. All three methods preserve the target distribution (i.e., they are lossless) and work with off-the-shelf models without requiring additional training or modifications. Empirically, on summarization, programming, and long-context tasks, our algorithms demonstrate significant speedups of up to 2.8x over standard autoregressive decoding. By enabling any off-the-shelf model to serve as a drafter and requiring no retraining, this work substantially broadens the applicability of the SD framework in practice.
|
Speculative Decoding, Large Language Models, Vocabulary Alignment, Heterogeneous Vocabularies, Efficient Inference, Inference Acceleration, Rejection Sampling, Tokenization, Transformer Architectures, Text Generation, Open Source.
| null | 15,148 |
2502.05202
|
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] |
https://github.com/keyboardAnt/hf-bench
|
4 |
LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models
|
https://openreview.net/forum?id=SyQPiZJVWY
|
[
"Parshin Shojaee",
"Ngoc-Hieu Nguyen",
"Kazem Meidani",
"Amir Barati Farimani",
"Khoa D Doan",
"Chandan K. Reddy"
] |
Oral
|
Scientific equation discovery is a fundamental task in the history of scientific progress, enabling the derivation of laws governing natural phenomena. Recently, Large Language Models (LLMs) have gained interest for this task due to their potential to leverage embedded scientific knowledge for hypothesis generation. However, evaluating the true discovery capabilities of these methods remains challenging, as existing benchmarks often rely on common equations that are susceptible to memorization by LLMs, leading to inflated performance metrics that do not reflect actual discovery. In this paper, we introduce LLM-SRBench, a comprehensive benchmark with 239 challenging problems across four scientific domains specifically designed to evaluate LLM-based scientific equation discovery methods while preventing trivial memorization. Our benchmark comprises two main categories: LSR-Transform, which transforms common physical models into less common mathematical representations to test reasoning beyond memorization, and LSR-Synth, which introduces synthetic, discovery-driven problems requiring data-driven reasoning. Through extensive evaluation of several state-of-the-art methods on LLM-SRBench, using both open and closed LLMs, we find that the best-performing system so far achieves only 31.5% symbolic accuracy.
These findings highlight the challenges of scientific equation discovery, positioning LLM-SRBench as a valuable resource for future research.
|
Benchmark, Scientific Discovery, Large Language Models, Symbolic Regression
|
We present LLM-SRBench, the first comprehensive benchmark for evaluating scientific equation discovery with LLMs, designed to rigorously assess discovery capabilities beyond memorization
| 14,812 | null |
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] |
https://github.com/deep-symbolic-mathematics/llm-srbench
|
5 |
ConceptAttention: Diffusion Transformers Learn Highly Interpretable Features
|
https://openreview.net/forum?id=Rc7y9HFC34
|
[
"Alec Helbling",
"Tuna Han Salih Meral",
"Benjamin Hoover",
"Pinar Yanardag",
"Duen Horng Chau"
] |
Oral
|
Do the rich representations of multi-modal diffusion transformers (DiTs) exhibit unique properties that enhance their interpretability? We introduce ConceptAttention, a novel method that leverages the expressive power of DiT attention layers to generate high-quality saliency maps that precisely locate textual concepts within images. Without requiring additional training, ConceptAttention repurposes the parameters of DiT attention layers to produce highly contextualized *concept embeddings*, contributing the major discovery that performing linear projections in the output space of DiT attention layers yields significantly sharper saliency maps compared to commonly used cross-attention maps. ConceptAttention even achieves state-of-the-art performance on zero-shot image segmentation benchmarks, outperforming 15 other zero-shot interpretability methods on the ImageNet-Segmentation dataset. ConceptAttention works for popular image models and even seamlessly generalizes to video generation. Our work contributes the first evidence that the representations of multi-modal DiTs are highly transferable to vision tasks like segmentation.
|
diffusion, interpretability, transformers, representation learning, mechanistic interpretability
|
We introduce a method for interpreting the representations of diffusion transformers by producing saliency maps of textual concepts.
| 14,767 |
2502.04320
|
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] |
https://github.com/helblazer811/ConceptAttention
|
6 |
Emergence in non-neural models: grokking modular arithmetic via average gradient outer product
|
https://openreview.net/forum?id=36hVB7DEB0
|
[
"Neil Rohit Mallinar",
"Daniel Beaglehole",
"Libin Zhu",
"Adityanarayanan Radhakrishnan",
"Parthe Pandit",
"Mikhail Belkin"
] |
Oral
|
Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply through a phase transition. In this work, we show that the phenomenon of grokking is not specific to neural networks nor to gradient descent-based optimization. Specifically, we show that this phenomenon occurs when learning modular arithmetic with Recursive Feature Machines (RFM), an iterative algorithm that uses the Average Gradient Outer Product (AGOP) to enable task-specific feature learning with general machine learning models. When used in conjunction with kernel machines, iterating RFM results in a fast transition from random, near zero, test accuracy to perfect test accuracy. This transition cannot be predicted from the training loss, which is identically zero, nor from the test loss, which remains constant in initial iterations. Instead, as we show, the transition is completely determined by feature learning: RFM gradually learns block-circulant features to solve modular arithmetic. Paralleling the results for RFM, we show that neural networks that solve modular arithmetic also learn block-circulant features. Furthermore, we present theoretical evidence that RFM uses such block-circulant features to implement the Fourier Multiplication Algorithm, which prior work posited as the generalizing solution neural networks learn on these tasks. Our results demonstrate that emergence can result purely from learning task-relevant features and is not specific to neural architectures nor gradient descent-based optimization methods. Furthermore, our work provides more evidence for AGOP as a key mechanism for feature learning in neural networks.
|
Theory of deep learning, grokking, modular arithmetic, feature learning, kernel methods, average gradient outer product (AGOP), emergence
|
We show that "emergence" in the task of grokking modular arithmetic occurs in feature learning kernels using the Average Gradient Outer Product (AGOP) and that the features take the form of block-circulant features.
| 14,743 |
2407.20199
|
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] |
https://github.com/nmallinar/rfm-grokking
|
7 |
Hierarchical Refinement: Optimal Transport to Infinity and Beyond
|
https://openreview.net/forum?id=EBNgREMoVD
|
[
"Peter Halmos",
"Julian Gold",
"Xinhao Liu",
"Benjamin Raphael"
] |
Oral
|
Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However, Sinkhorn has quadratic space complexity in the number of points, limiting scalability to larger datasets. Low-rank OT achieves linear-space complexity, but by definition, cannot compute a one-to-one correspondence between points. When the optimal transport problem is an assignment problem between datasets then an optimal mapping, known as the _Monge map_, is guaranteed to be a bijection. In this setting, we show that the factors of an optimal low-rank coupling co-cluster each point with its image under the Monge map. We leverage this invariant to derive an algorithm,
_Hierarchical Refinement_ (`HiRef`), that dynamically constructs a multiscale partition of each dataset using low-rank OT subproblems, culminating in a bijective coupling. Hierarchical Refinement uses linear space and has log-linear runtime, retaining the space advantage of low-rank OT while overcoming its limited resolution. We demonstrate the advantages of Hierarchical Refinement on several datasets, including ones containing over a million points, scaling full-rank OT to problems previously beyond Sinkhorn's reach.
|
Optimal transport, low-rank, linear complexity, sparse, full-rank
|
Linear-complexity optimal transport, using low-rank optimal transport to progressively refine the solution to a Monge map.
| 14,649 |
2503.03025
|
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] |
https://github.com/raphael-group/HiRef
|
8 |
Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions
|
https://openreview.net/forum?id=DjJmre5IkP
|
[
"Jaeyeon Kim",
"Kulin Shah",
"Vasilis Kontonis",
"Sham M. Kakade",
"Sitan Chen"
] |
Oral
|
In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from $<7$\% to $\approx 90$\%, even outperforming ARMs that were explicitly trained via teacher forcing to learn the right order of decoding.
|
Discrete Diffusion models, Masked Diffusion Models, Diffusion Models, Learning Theory, Inference-Time Strategy
| null | 14,095 |
2502.06768
|
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] | null |
9 |
Statistical Test for Feature Selection Pipelines by Selective Inference
|
https://openreview.net/forum?id=4EYwwVuhtG
|
[
"Tomohiro Shiraishi",
"Tatsuya Matsukawa",
"Shuichi Nishino",
"Ichiro Takeuchi"
] |
Oral
|
A data analysis pipeline is a structured sequence of steps that transforms raw data into meaningful insights by integrating various analysis algorithms. In this paper, we propose a novel statistical test to assess the significance of data analysis pipelines. Our approach enables the systematic development of valid statistical tests applicable to any feature selection pipeline composed of predefined components. We develop this framework based on selective inference, a statistical technique that has recently gained attention for data-driven hypotheses. As a proof of concept, we focus on feature selection pipelines for linear models, composed of three missing value imputation algorithms, three outlier detection algorithms, and three feature selection algorithms. We theoretically prove that our statistical test can control the probability of false positive feature selection at any desired level, and demonstrate its validity and effectiveness through experiments on synthetic and real data. Additionally, we present an implementation framework that facilitates testing across any configuration of these feature selection pipelines without extra implementation costs.
|
Data Analysis Pipeline, AutoML, Statistical Test, Selective Inference, Missing Value Imputation, Outlier Detection, Feature Selection
|
We introduce a statistical test for data analysis pipeline in feature selection problems, which allows for the systematic development of valid statistical tests applicable to any pipeline configuration composed of a set of predefined components.
| 13,925 |
2406.18902
|
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https://github.com/Takeuchi-Lab-SI-Group/si4pipeline
|
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