ICLR 2024 论文列表

International Conference on Learning Representations

录用类型

2,260篇论文

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  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

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Pre-training Sequence, Structure, and Surface Features for Comprehensive Protein Representation Learning

Youhan Lee, Hasun Yu, Jaemyung Lee, Jaehoon Kim

展开摘要

Proteins can be represented in various ways, including their sequences, 3D structures, and surfaces. While recent studies have successfully employed sequence- or structure-based representations to address multiple tasks in protein science, there has been significant oversight in incorporating protein surface information, a critical factor for protein function. In this paper, we present a pre-training strategy that incorporates information from protein sequences, 3D structures, and surfaces to improve protein representation learning. Specifically, we utilize Implicit Neural Representations (INRs) for learning surface characteristics, and name it ProteinINR. We confirm that ProteinINR successfully reconstructs protein surfaces, and integrate this surface learning into the existing pre-training strategy of sequences and structures. Our results demonstrate that our approach can enhance performance in various downstream tasks, thereby underscoring the importance of including surface attributes in protein representation learning. These findings underline the importance of understanding protein surfaces for generating effective protein representations.

Poster
A Unified and General Framework for Continual Learning

Zhenyi Wang, Yan Li, Li Shen, Heng Huang

展开摘要

Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including regularization-based, Bayesian-based, and memory-replay-based techniques. However, these methods lack a unified framework and common terminology for describing their approaches. This research aims to bridge this gap by introducing a comprehensive and overarching framework that encompasses and reconciles these existing methodologies. Notably, this new framework is capable of encompassing established CL approaches as special instances within a unified and general optimization objective. An intriguing finding is that despite their diverse origins, these methods share common mathematical structures. This observation highlights the compatibility of these seemingly distinct techniques, revealing their interconnectedness through a shared underlying optimization objective. Moreover, the proposed general framework introduces an innovative concept called *refresh learning*, specifically designed to enhance the CL performance. This novel approach draws inspiration from neuroscience, where the human brain often sheds outdated information to improve the retention of crucial knowledge and facilitate the acquisition of new information. In essence, *refresh learning* operates by initially unlearning current data and subsequently relearning it. It serves as a versatile plug-in that seamlessly integrates with existing CL methods, offering an adaptable and effective enhancement to the learning process. Extensive experiments on CL benchmarks and theoretical analysis demonstrate the effectiveness of the proposed *refresh learning*.

Poster
Hybrid Directional Graph Neural Network for Molecules

Junyi An, Chao Qu, Zhipeng Zhou, Fenglei Cao, Xu Yinghui, Yuan Qi, Furao Shen

展开摘要

Equivariant message passing neural networks have emerged as the prevailing approach for predicting chemical properties of molecules due to their ability to leverage translation and rotation symmetries, resulting in a strong inductive bias. However, the equivariant operations in each layer can impose excessive constraints on the function form and network flexibility. To address these challenges, we introduce a novel network called the Hybrid Directional Graph Neural Network (HDGNN), which effectively combines strictly equivariant operations with learnable modules. We evaluate the performance of HDGNN on the QM9 dataset and the IS2RE dataset of OC20, demonstrating its state-of-the-art performance on several tasks and competitive performance on others. Our code is anonymously released on https://github.com/ajy112/HDGNN.

Spotlight
Compressing LLMs: The Truth is Rarely Pure and Never Simple

AJAY KUMAR JAISWAL, Zhe Gan, Xianzhi Du, Bowen Zhang, Zhangyang Wang, Yinfei Yang

展开摘要

Despite their remarkable achievements, modern Large Language Models (LLMs) encounter exorbitant computational and memory footprints. Recently, several works have shown significant success in *training-free* and *data-free* compression (pruning and quantization) of LLMs achieving 50-60\% sparsity and reducing the bit-width down to 3 or 4 bits per weight, with negligible perplexity degradation over the uncompressed baseline. As recent research efforts are focused on developing increasingly sophisticated compression methods, our work takes a step back, and re-evaluates the effectiveness of existing SoTA compression methods, which rely on a fairly simple and widely questioned metric, perplexity (even for dense LLMs). We introduce **K**nowledge-**I**ntensive **C**ompressed LLM Benchmar**K** **(LLM-KICK)**, a collection of carefully-curated tasks to re-define the evaluation protocol for compressed LLMs, which have significant alignment with their dense counterparts, and perplexity fail to capture subtle change in their true capabilities. LLM-KICK unveils many favorable merits and unfortunate plights of current SoTA compression methods: all pruning methods suffer significant performance degradation, sometimes at trivial sparsity ratios (*e.g.*, 25-30\%), and fail for N:M sparsity on knowledge-intensive tasks; current quantization methods are more successful than pruning; yet, pruned LLMs even at $\geq 50$\% sparsity are robust in-context retrieval and summarization systems; among others. LLM-KICK is designed to holistically access compressed LLMs' ability for language understanding, reasoning, generation, in-context retrieval, in-context summarization, *etc.* We hope our study can foster the development of better LLM compression methods. The reproduced codes are available at https://github.com/VITA-Group/llm-kick.

Poster
ToolChain*: Efficient Action Space Navigation in Large Language Models with A* Search

Yuchen Zhuang, Xiang Chen, Tong Yu, Saayan Mitra, Victor Bursztyn, Ryan A. Rossi, Somdeb Sarkhel, Chao Zhang

展开摘要

Large language models (LLMs) have demonstrated powerful decision-making and planning capabilities in solving complicated real-world problems. LLM-based autonomous agents can interact with diverse tools (e.g., functional APIs) and generate solution plans that execute a series of API function calls in a step-by-step manner. The multitude of candidate API function calls significantly expands the action space, amplifying the critical need for efficient action space navigation. However, existing methods either struggle with unidirectional exploration in expansive action spaces, trapped into a locally optimal solution, or suffer from exhaustively traversing all potential actions, causing inefficient navigation. To address these issues, we propose ToolChain*, an efficient tree search-based planning algorithm for LLM-based agents. It formulates the entire action space as a decision tree, where each node represents a possible API function call involved in a solution plan. By incorporating the A$^*$ search algorithm with task-specific cost function design, it efficiently prunes high-cost branches that may involve incorrect actions, identifying the most low-cost valid path as the solution. Extensive experiments on multiple tool-use and reasoning tasks demonstrate that ToolChain* efficiently balances exploration and exploitation within an expansive action space. It outperforms state-of-the-art baselines on planning and reasoning tasks by 3.1% and 3.5% on average while requiring 7.35x and 2.31x less time, respectively.

Poster
P2Seg: Pointly-supervised Segmentation via Mutual Distillation

Zipeng Wang, Xuehui Yu, Xumeng Han, Wenwen Yu, Zhixun Huang, Jianbin Jiao, Zhenjun Han

展开摘要

Point-level Supervised Instance Segmentation (PSIS) aims to enhance the applicability and scalability of instance segmentation by utilizing low-cost yet instance-informative annotations. Existing PSIS methods usually rely on positional information to distinguish objects, but predicting precise boundaries remains challenging due to the lack of contour annotations. Nevertheless, weakly supervised semantic segmentation methods are proficient in utilizing intra-class feature consistency to capture the boundary contours of the same semantic regions. In this paper, we design a Mutual Distillation Module (MDM) to leverage the complementary strengths of both instance position and semantic information and achieve accurate instance-level object perception. The MDM consists of Semantic to Instance (S2I) and Istance to Semantic (I2S). S2I is guided by the precise boundaries of semantic regions to learn the association between annotated points and instance contours. I2S leverages discriminative relationships between instances to facilitate the differentiation of various objects within the semantic map. Extensive experiments substantiate the efficacy of MDM in fostering the synergy between instance and semantic information, consequently improving the quality of instance-level object representations. Our method achieves 55.7 mAP50 and 17.6 mAP on the PASCAL VOC and MS COCO datasets, significantly outperforming recent PSIS methods and several box-supervised instance segmentation competitors.

Poster
Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood

Yaxuan Zhu, Jianwen Xie, Ying Nian Wu, Ruiqi Gao

展开摘要

Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming, and there exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the two models are jointly estimated within a cooperative training framework: Samples from the initializer serve as starting points that are refined by a few MCMC sampling steps from the EBM. The EBM is then optimized by maximizing recovery likelihood, while the initializer model is optimized by learning from the difference between the refined samples and the initial samples. In addition, we made several practical designs for EBM training to further improve the sample quality. Combining these advances, we significantly boost the generation performance compared to existing EBM methods on CIFAR-10 and ImageNet 32x32. And we have shown that CDRL has great potential to largely reduce the sampling time. We also demonstrate the effectiveness of our models for several downstream tasks, including classifier-free guided generation, compositional generation, image inpainting and out-of-distribution detection.

Spotlight
Symmetric Neural-Collapse Representations with Supervised Contrastive Loss: The Impact of ReLU and Batching

Ganesh Ramachandra Kini, Vala Vakilian, Tina Behnia, Jaidev Gill, Christos Thrampoulidis

展开摘要

Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced data, this symmetry breaks under class imbalances. This paper presents an intriguing discovery: the introduction of a ReLU activation at the final layer effectively restores the symmetry in SCL-learned representations. We arrive at this finding analytically, by establishing that the global minimizers of an unconstrained features model with SCL loss and entry-wise non-negativity constraints form an orthogonal frame. Extensive experiments conducted across various datasets, architectures, and imbalance scenarios corroborate our finding. Importantly, our experiments reveal that the inclusion of the ReLU activation restores symmetry without compromising test accuracy. This constitutes the first geometry characterization of SCL under imbalances. Additionally, our analysis and experiments underscore the pivotal role of batch selection strategies in representation geometry. By proving necessary and sufficient conditions for mini-batch choices that ensure invariant symmetric representations, we introduce batch-binding as an efficient strategy that guarantees these conditions hold.

Poster
Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression

Runtian Zhai, Bingbin Liu, Andrej Risteski, J Zico Kolter, Pradeep Kumar Ravikumar

展开摘要

Data augmentation is critical to the empirical success of modern self-supervised representation learning, such as contrastive learning and masked language modeling. However, a theoretical understanding of the exact role of the augmentation remains limited. Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator, suggesting that learning a linear probe atop such representation can be connected to RKHS regression. Building on this insight, this work delves into a statistical analysis of augmentation-based pretraining. Starting from the isometry property, a geometric characterization of the target function given by the augmentation, we disentangle the effects of the model and the augmentation, and prove two generalization bounds that are free of model complexity. Our first bound works for an arbitrary encoder, and it is the sum of an estimation error bound incurred by fitting a linear probe, and an approximation error bound by RKHS approximation. Our second bound specifically addresses the case where the encoder extracts the top-d eigenspace of a finite-sample-based approximation of the underlying RKHS. A key ingredient in our analysis is the *augmentation complexity*, which we use to quantitatively compare different augmentations and analyze their impact on downstream performance.

Spotlight
Function Vectors in Large Language Models

Eric Todd, Millicent Li, Arnab Sen Sharma, Aaron Mueller, Byron C Wallace, David Bau

展开摘要

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Our findings show that compact, causal internal vector representations of function abstractions can be explicitly extracted from LLMs.

Poster
What Algorithms can Transformers Learn? A Study in Length Generalization

Hattie Zhou, Arwen Bradley, Etai Littwin, Noam Razin, Omid Saremi, Joshua M. Susskind, Samy Bengio, Preetum Nakkiran

展开摘要

Large language models exhibit surprising emergent generalization properties, yet also struggle on many simple reasoning tasks such as arithmetic and parity. In this work, we focus on length generalization, and we propose a unifying framework to understand when and how Transformers can be expected to length generalize on a given task. First, we show that there exist algorithmic tasks for which standard decoder-only Transformers trained from scratch naturally exhibit strong length generalization. For these tasks, we leverage the RASP programming language (Weiss et al., 2021) to show that the correct algorithmic solution which solves the task can be represented by a simple Transformer. We thus propose the RASP-Generalization Conjecture: Transformers tend to learn a length-generalizing solution if there exists a short RASP-L program that works for all input lengths. We present empirical evidence to support the correlation between RASP-simplicity and generalization. We leverage our insights to give new scratchpad formats which yield strong length generalization on traditionally hard tasks (such as parity and addition), and we illustrate how scratchpad can hinder generalization when it increases the complexity of the corresponding RASP-L program. Overall, our work provides a novel perspective on the mechanisms of length generalization and the algorithmic capabilities of Transformers.

Poster
FairTune: Optimizing Parameter Efficient Fine Tuning for Fairness in Medical Image Analysis

Raman Dutt, Ondrej Bohdal, Sotirios A. Tsaftaris, Timothy Hospedales

展开摘要

Training models with robust group fairness properties is crucial in ethically sensitive application areas such as medical diagnosis. Despite the growing body of work aiming to minimise demographic bias in AI, this problem remains challenging. A key reason for this challenge is the fairness generalisation gap: High-capacity deep learning models can fit all training data nearly perfectly, and thus also exhibit perfect fairness during training. In this case, bias emerges only during testing when generalisation performance differs across sub-groups. This motivates us to take a bi-level optimisation perspective on fair learning: Optimising the learning strategy based on validation fairness. Specifically, we consider the highly effective workflow of adapting pre-trained models to downstream medical imaging tasks using parameter-efficient fine-tuning (PEFT) techniques. There is a trade-off between updating more parameters, enabling a better fit to the task of interest vs. fewer parameters, potentially reducing the generalisation gap. To manage this tradeoff, we propose FairTune, a framework to optimise the choice of PEFT parameters with respect to fairness. We demonstrate empirically that FairTune leads to improved fairness on a range of medical imaging datasets. The code is available at https://github.com/Raman1121/FairTune.

Poster
KoLA: Carefully Benchmarking World Knowledge of Large Language Models

Jifan Yu, Xiaozhi Wang, Shangqing Tu, Shulin Cao, Daniel Zhang-Li, Xin Lv, Hao Peng, Zijun Yao, Xiaohan Zhang, Hanming Li, Chunyang Li, Zheyuan Zhang, Yushi Bai, Yantao Liu, Amy Xin, Kaifeng Yun, Linlu GONG, Nianyi Lin, Jianhui Chen, Zhili Wu, Yunjia Qi, Weikai Li, Yong Guan, Kaisheng Zeng, Ji Qi, Hailong Jin, Jinxin Liu, Yu Gu, Yuan Yao, Ning Ding, Lei Hou, Zhiyuan Liu, Xu Bin, Jie Tang, Juanzi Li

展开摘要

The unprecedented performance of large language models (LLMs) necessitates improvements in evaluations. Rather than merely exploring the breadth of LLM abilities, we believe meticulous and thoughtful designs are essential to thorough, unbiased, and applicable evaluations. Given the importance of world knowledge to LLMs, we construct a Knowledge-oriented LLM Assessment benchmark (KoLA), in which we carefully design three crucial factors: (1) For ability modeling, we mimic human cognition to form a four-level taxonomy of knowledge-related abilities, covering 19 tasks. (2) For data, to ensure fair comparisons, we use both Wikipedia, a corpus prevalently pre-trained by LLMs, along with continuously collected emerging corpora, aiming to evaluate the capacity to handle unseen data and evolving knowledge. (3) For evaluation criteria, we adopt a contrastive system, including overall standard scores for better numerical comparability across tasks and models, and a unique self-contrast metric for automatically evaluating knowledge-creating ability. We evaluate 21 open-source and commercial LLMs and obtain some intriguing findings. The KoLA dataset will be updated every three months to provide timely references for developing LLMs and knowledge-related systems.

Poster
Critical Learning Periods Emerge Even in Deep Linear Networks

Michael Kleinman, Alessandro Achille, Stefano Soatto

展开摘要

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks, critical learning periods have been empirically observed in both systems. This suggests that critical periods may be fundamental to learning and not an accident of biology. Yet, why exactly critical periods emerge in deep networks is still an open question, and in particular it is unclear whether the critical periods observed in both systems depend on particular architectural or optimization details. To isolate the key underlying factors, we focus on deep linear network models, and show that, surprisingly, such networks also display much of the behavior seen in biology and artificial networks, while being amenable to analytical treatment. We show that critical periods depend on the depth of the model and structure of the data distribution. We also show analytically and in simulations that the learning of features is tied to competition between sources. Finally, we extend our analysis to multi-task learning to show that pre-training on certain tasks can damage the transfer performance on new tasks, and show how this depends on the relationship between tasks and the duration of the pre-training stage. To the best of our knowledge, our work provides the first analytically tractable model that sheds light into why critical learning periods emerge in biological and artificial networks.

Spotlight
How Well Do Supervised 3D Models Transfer to Medical Imaging Tasks?

Wenxuan Li, Alan Yuille, Zongwei Zhou

展开摘要

The pre-training and fine-tuning paradigm has become prominent in transfer learning. For example, if the model is pre-trained on ImageNet and then fine-tuned to PASCAL, it can significantly outperform that trained on PASCAL from scratch. While ImageNet pre-training has shown enormous success, it is formed in 2D, and the learned features are for classification tasks; when transferring to more diverse tasks, like 3D image segmentation, its performance is inevitably compromised due to the deviation from the original ImageNet context. A significant challenge lies in the lack of large, annotated 3D datasets rivaling the scale of ImageNet for model pre-training. To overcome this challenge, we make two contributions. Firstly, we construct AbdomenAtlas 1.1 that comprises **9,262** three-dimensional computed tomography (CT) volumes with high-quality, per-voxel annotations of 25 anatomical structures and pseudo annotations of seven tumor types. Secondly, we develop a suite of models that are pre-trained on our AbdomenAtlas 1.1 for transfer learning. Our preliminary analyses indicate that the model trained only with 21 CT volumes, 672 masks, and 40 GPU hours has a transfer learning ability similar to the model trained with 5,050 (unlabeled) CT volumes and 1,152 GPU hours. More importantly, the transfer learning ability of supervised models can further scale up with larger annotated datasets, achieving significantly better performance than preexisting pre-trained models, irrespective of their pre-training methodologies or data sources. We hope this study can facilitate collective efforts in constructing larger 3D medical datasets and more releases of supervised pre-trained models.

Oral
BatchPrompt: Accomplish more with less

Jianzhe Lin, Maurice Diesendruck, Liang Du, Robin Abraham

展开摘要

The ever-increasing token limits of large language models (LLMs) have enabled long context as input. Many LLMs are trained and fine-tuned to perform zero/few-shot inference using instruction-based prompts. Prompts typically include a detailed task instruction, several examples, and a single data point for inference. This baseline is referred to as “SinglePrompt” in this paper. In terms of token count, when the data input is small compared to instructions and examples, this results in lower token utilization, compared with encoder-based models like fine-tuned BERT. This cost inefficiency, affecting inference speed and compute budget, counteracts many of the benefits that LLMs offer. This paper aims to alleviate this problem by batching multiple data points in each prompt, a strategy we refer to as “BatchPrompt”. We improve token utilization by increasing the “density” of data points, however, this cannot be done naively. Simple batching can degrade performance, especially as batch size increases, and data points can yield different answers depending on their position within a prompt. To address the quality issue while retaining high token utilization, we introduce Batch Permutation and Ensembling (BPE) for BatchPrompt – a simple majority vote over repeated permutations of data, that recovers label quality at the cost of more token usage. To counterbalance this cost, we further propose Self-reflection-guided EArly Stopping (SEAS), which can terminate the voting process early for data points that the LLM handles confidently. Our comprehensive experimental evaluation demonstrates that BPE + SEAS can boost the performance of BatchPrompt by a striking margin on a range of popular NLP tasks, including question answering (Boolq), textual entailment (RTE), and duplicate questions identification (QQP). This performance is even competitive with/higher than single-data prompting (SinglePrompt), while using far fewer LLM calls and input tokens. At batch size 32, our BatchPrompt + BPE + SEAS uses 15.7% the number of LLM calls, and achieves: Boolq accuracy 90.6% → 90.9% with 27.4% tokens, QQP accuracy 87.2% → 88.4% with 18.6% tokens, RTE accuracy 91.5% → 91.1% with 30.8% tokens. We hope our simple yet effective approach will shed light on the future research of large language models. Code: github.com/microsoft/BatchPrompt

Poster
OMNI: Open-endedness via Models of human Notions of Interestingness

Jenny Zhang, Joel Lehman, Kenneth Stanley, Jeff Clune

展开摘要

Open-ended algorithms aim to learn new, interesting behaviors forever. That requires a vast environment search space, but there are thus infinitely many possible tasks. Even after filtering for tasks the current agent can learn (i.e., learning progress), countless learnable yet uninteresting tasks remain (e.g., minor variations of previously learned tasks). An Achilles Heel of open-endedness research is the inability to quantify (and thus prioritize) tasks that are not just learnable, but also $\textit{interesting}$ (e.g., worthwhile and novel). We propose solving this problem by $\textit{Open-endedness via Models of human Notions of Interestingness}$ (OMNI). The insight is that we can utilize foundation models (FMs) as a model of interestingness (MoI), because they $\textit{already}$ internalize human concepts of interestingness from training on vast amounts of human-generated data, where humans naturally write about what they find interesting or boring. We show that FM-based MoIs improve open-ended learning by focusing on tasks that are both learnable $\textit{and interesting}$, outperforming baselines based on uniform task sampling or learning progress alone. This approach has the potential to dramatically advance the ability to intelligently select which tasks to focus on next (i.e., auto-curricula), and could be seen as AI selecting its own next task to learn, facilitating self-improving AI and AI-Generating Algorithms.

Poster
Large Language Models as Analogical Reasoners

Michihiro Yasunaga, Xinyun Chen, Yujia Li, Panupong Pasupat, Jure Leskovec, Percy Liang, Ed H. Chi, Denny Zhou

展开摘要

Chain-of-thought (CoT) prompting for language models demonstrates impressive performance across reasoning tasks, but typically needs labeled exemplars of the reasoning process. In this work, we introduce a new prompting approach, analogical prompting, designed to automatically guide the reasoning process of large language models. Inspired by analogical reasoning, a cognitive process in which humans draw from relevant past experiences to tackle new problems, our approach prompts language models to self-generate relevant exemplars or knowledge in the context, before proceeding to solve the given problem. This method presents several advantages: it obviates the need for labeling or retrieving exemplars, offering generality and convenience; it can also tailor the generated exemplars and knowledge to each problem, offering adaptability. Experimental results show that our approach outperforms 0-shot CoT and manual few-shot CoT in a variety of reasoning tasks, including math problem solving in GSM8K and MATH, code generation in Codeforces, and other reasoning tasks in BIG-Bench.

Poster
Role of Locality and Weight Sharing in Image-Based Tasks: A Sample Complexity Separation between CNNs, LCNs, and FCNs

Aakash Lahoti, Stefani Karp, Ezra Winston, Aarti Singh, Yuanzhi Li

展开摘要

Vision tasks are characterized by the properties of locality and translation invariance. The superior performance of convolutional neural networks (CNNs) on these tasks is widely attributed to the inductive bias of locality and weight sharing baked into their architecture. Existing attempts to quantify the statistical benefits of these biases in CNNs over locally connected convolutional neural networks (LCNs) and fully connected neural networks (FCNs) fall into one of the following categories: either they disregard the optimizer and only provide uniform convergence upper bounds with no separating lower bounds, or they consider simplistic tasks that do not truly mirror the locality and translation invariance as found in real-world vision tasks. To address these deficiencies, we introduce the Dynamic Signal Distribution (DSD) classification task that models an image as consisting of $k$ patches, each of dimension $d$, and the label is determined by a $d$-sparse signal vector that can freely appear in any one of the $k$ patches. On this task, for any orthogonally equivariant algorithm like gradient descent, we prove that CNNs require $\tilde{O}(k+d)$ samples, whereas LCNs require $\Omega(kd)$ samples, establishing the statistical advantages of weight sharing in translation invariant tasks. Furthermore, LCNs need $\tilde{O}(k(k+d))$ samples, compared to $\Omega(k^2d)$ samples for FCNs, showcasing the benefits of locality in local tasks. Additionally, we develop information theoretic tools for analyzing randomized algorithms, which may be of interest for statistical research.

Spotlight
General Stability Analysis for Zeroth-Order Optimization Algorithms

Xinyue Liu, Hualin Zhang, Bin Gu, Hong Chen

展开摘要

Zeroth-order optimization algorithms are widely used for black-box optimization problems, such as those in machine learning and prompt engineering, where the gradients are approximated using function evaluations. Recently, a generalization result was provided for zeroth-order stochastic gradient descent (SGD) algorithms through stability analysis. However, this result was limited to the vanilla 2-point zeroth-order estimate of Gaussian distribution used in SGD algorithms. To address these limitations, we propose a general proof framework for stability analysis that applies to convex, strongly convex, and non-convex conditions, and yields results for popular zeroth-order optimization algorithms, including SGD, GD, and SVRG, as well as various zeroth-order estimates, such as 1-point and 2-point with different distributions and coordinate estimates. Our general analysis shows that coordinate estimation can lead to tighter generalization bounds for SGD, GD, and SVRG versions of zeroth-order optimization algorithms, due to the smaller expansion brought by coordinate estimates to stability analysis.

Poster