NeurIPS 2023 论文列表

Conference on Neural Information Processing Systems

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3,584篇论文

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Nonparametric Identifiability of Causal Representations from Unknown Interventions

Julius Von Kügelgen, Michel Besserve, Wendong Liang, Luigi Gresele, Armin Kekić, Elias Bareinboim, David Blei, Bernhard Schölkopf

展开摘要

We study causal representation learning, the task of inferring latent causal variables and their causal relations from high-dimensional functions (“mixtures”) of the variables. Prior work relies on weak supervision, in the form of counterfactual pre- and post-intervention views or temporal structure; places restrictive assumptions, such as linearity, on the mixing function or latent causal model; or requires partial knowledge of the generative process, such as the causal graph or intervention targets. We instead consider the general setting in which both the causal model and the mixing function are nonparametric. The learning signal takes the form of multiple datasets, or environments, arising from unknown interventions in the underlying causal model. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data. We study the fundamental setting of two causal variables and prove that the observational distribution and one perfect intervention per node suffice for identifiability, subject to a genericity condition. This condition rules out spurious solutions that involve fine-tuning of the intervened and observational distributions, mirroring similar conditions for nonlinear cause-effect inference. For an arbitrary number of variables, we show that at least one pair of distinct perfect interventional domains per node guarantees identifiability. Further, we demonstrate that the strengths of causal influences among the latent variables are preserved by all equivalent solutions, rendering the inferred representation appropriate for drawing causal conclusions from new data. Our study provides the first identifiability results for the general nonparametric setting with unknown interventions, and elucidates what is possible and impossible for causal representation learning without more direct supervision.

Poster
SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models

Martin Gonzalez, Nelson Fernandez, Thuy Vinh Dinh Tran, Elies Gherbi, Hatem Hajri, Nader Masmoudi

展开摘要

A potent class of generative models known as Diffusion Probabilistic Models (DPMs) has become prominent. A forward diffusion process adds gradually noise to data, while a model learns to gradually denoise. Sampling from pre-trained DPMs is obtained by solving differential equations (DE) defined by the learnt model, a process which has shown to be prohibitively slow. Numerous efforts on speeding-up this process have consisted on crafting powerful ODE solvers. Despite being quick, such solvers do not usually reach the optimal quality achieved by available slow SDE solvers. Our goal is to propose SDE solvers that reach optimal quality without requiring several hundreds or thousands of NFEs to achieve that goal. We propose Stochastic Explicit Exponential Derivative-free Solvers (SEEDS), improving and generalizing Exponential Integrator approaches to the stochastic case on several frameworks. After carefully analyzing the formulation of exact solutions of diffusion SDEs, we craft SEEDS to analytically compute the linear part of such solutions. Inspired by the Exponential Time-Differencing method, SEEDS use a novel treatment of the stochastic components of solutions, enabling the analytical computation of their variance, and contains high-order terms allowing to reach optimal quality sampling $\sim3$-$5\times$ faster than previous SDE methods. We validate our approach on several image generation benchmarks, showing that SEEDS outperform or are competitive with previous SDE solvers. Contrary to the latter, SEEDS are derivative and training free, and we fully prove strong convergence guarantees for them.

Poster
Localized Symbolic Knowledge Distillation for Visual Commonsense Models

Jae Sung Park, Jack Hessel, Khyathi Chandu, Paul Pu Liang, Ximing Lu, Peter West, Youngjae Yu, Qiuyuan Huang, Jianfeng Gao, Ali Farhadi, Yejin Choi

展开摘要

Instruction following vision-language (VL) models offer a flexible interface that supports a broad range of multimodal tasks in a zero-shot fashion. However, interfaces that operate on full images do not directly enable the user to “point to" and access specific regions within images. This capability is important not only to support reference-grounded VL benchmarks, but also, for practical applications that require precise within-image reasoning. We build Localized Visual Commonsense model which allows users to specify (multiple) regions- as-input. We train our model by sampling localized commonsense knowledge from a large language model (LLM): specifically, we prompt a LLM to collect commonsense knowledge given a global literal image description and a local literal region description automatically generated by a set of VL models. This pipeline is scalable and fully automatic, as no aligned or human-authored image and text pairs are required. With a separately trained critic model that selects high quality examples, we find that training on the localized commonsense corpus expanded solely from images can successfully distill existing VL models to support a reference-as-input interface. Empirical results and human evaluations in zero-shot settings demonstrate that our distillation method results in more precise VL models of reasoning compared to a baseline of passing a generated referring expression.

Poster
Lockdown: Backdoor Defense for Federated Learning with Isolated Subspace Training

Tiansheng Huang, Sihao Hu, Ka-Ho Chow, Fatih Ilhan, Selim Furkan Tekin, Ling Liu

展开摘要

Federated learning (FL) is vulnerable to backdoor attacks due to its distributed computing nature. Existing defense solution usually requires larger amount of computation in either the training or testing phase, which limits their practicality in the resource-constrain scenarios. A more practical defense, i.e., neural network (NN) pruning based defense has been proposed in centralized backdoor setting. However, our empirical study shows that traditional pruning-based solution suffers \textit{poison-coupling} effect in FL, which significantly degrades the defense performance.This paper presents Lockdown, an isolated subspace training method to mitigate the poison-coupling effect. Lockdown follows three key procedures. First, it modifies the training protocol by isolating the training subspaces for different clients. Second, it utilizes randomness in initializing isolated subspacess, and performs subspace pruning and subspace recovery to segregate the subspaces between malicious and benign clients. Third, it introduces quorum consensus to cure the global model by purging malicious/dummy parameters. Empirical results show that Lockdown achieves \textit{superior} and \textit{consistent} defense performance compared to existing representative approaches against backdoor attacks. Another value-added property of Lockdown is the communication-efficiency and model complexity reduction, which are both critical for resource-constrain FL scenario. Our code is available at \url{https://github.com/git-disl/Lockdown}.

Poster
Causal Effect Regularization: Automated Detection and Removal of Spurious Correlations

Abhinav Kumar, Amit Deshpande, Amit Sharma

展开摘要

In many classification datasets, the task labels are spuriously correlated with some input attributes. Classifiers trained on such datasets often rely on these attributes for prediction, especially when the spurious correlation is high, and thus fail to generalize whenever there is a shift in the attributes’ correlation at deployment. If we assume that the spurious attributes are known a priori, several methods have been proposed to learn a classifier that is invariant to the specified attributes. However, in real-world data, information about spurious attributes is typically unavailable. Therefore, we propose a method that automatically identifies spurious attributes by estimating their causal effect on the label and then uses a regularization objective to mitigate the classifier’s reliance on them. Although causal effect of an attribute on the label is not always identified, we present two commonly occurring data-generating processes where the effect can be identified. Compared to recent work for identifying spurious attributes, we find that our method, AutoACER, is more accurate in removing the attribute from the learned model, especially when spurious correlation is high. Specifically, across synthetic, semi-synthetic, and real-world datasets, AutoACER shows significant improvement in a metric used to quantify the dependence of a classifier on spurious attributes ($\Delta$Prob), while obtaining better or similar accuracy. Empirically we find that AutoACER mitigates the reliance on spurious attributes even under noisy estimation of causal effects or when the causal effect is not identified. To explain the empirical robustness of our method, we create a simple linear classification task with two sets of attributes: causal and spurious. Under this setting, we prove that AutoACER only requires the ranking of estimated causal effects to be correct across attributes to select the correct classifier.

Poster
Strategic Behavior in Two-sided Matching Markets with Prediction-enhanced Preference-formation

Stefania Ionescu, Yuhao Du, Kenneth Joseph, Aniko Hannak

展开摘要

Two-sided matching markets have long existed to pair agents in the absence of regulated exchanges. A common example is school choice, where a matching mechanism uses student and school preferences to assign students to schools. In such settings, forming preferences is both difficult and critical. Prior work has suggested various prediction mechanisms that help agents make decisions about their preferences. Although often deployed together, these matching and prediction mechanisms are almost always analyzed separately. The present work shows that at the intersection of the two lies a previously unexplored type of strategic behavior: agents returning to the market (e.g., schools) can attack future predictions by interacting short-term non-optimally with their matches. Here, we first introduce this type of strategic behavior, which we call an adversarial interaction attack. Next, we construct a formal economic model that captures the feedback loop between prediction mechanisms designed to assist agents and the matching mechanism used to pair them. Finally, in a simplified setting, we prove that returning agents can benefit from using adversarial interaction attacks and gain progressively more as the trust in and accuracy of predictions increases. We also show that this attack increases inequality in the student population.

Poster
Perceptual Kalman Filters: Online State Estimation under a Perfect Perceptual-Quality Constraint

Dror Freirich, Tomer Michaeli, Ron Meir

展开摘要

Many practical settings call for the reconstruction of temporal signals from corrupted or missing data. Classic examples include decoding, tracking, signal enhancement and denoising. Since the reconstructed signals are ultimately viewed by humans, it is desirable to achieve reconstructions that are pleasing to human perception. Mathematically, perfect perceptual-quality is achieved when the distribution of restored signals is the same as that of natural signals, a requirement which has been heavily researched in static estimation settings (i.e. when a whole signal is processed at once). Here, we study the problem of optimal causal filtering under a perfect perceptual-quality constraint, which is a task of fundamentally different nature. Specifically, we analyze a Gaussian Markov signal observed through a linear noisy transformation. In the absence of perceptual constraints, the Kalman filter is known to be optimal in the MSE sense for this setting. Here, we show that adding the perfect perceptual quality constraint (i.e. the requirement of temporal consistency), introduces a fundamental dilemma whereby the filter may have to ``knowingly'' ignore new information revealed by the observations in order to conform to its past decisions. This often comes at the cost of a significant increase in the MSE (beyond that encountered in static settings). Our analysis goes beyond the classic innovation process of the Kalman filter, and introduces the novel concept of an unutilized information process. Using this tool, we present a recursive formula for perceptual filters, and demonstrate the qualitative effects of perfect perceptual-quality estimation on a video reconstruction problem.

Poster
Temporal Conditioning Spiking Latent Variable Models of the Neural Response to Natural Visual Scenes

Gehua Ma, Runhao Jiang, Rui Yan, Huajin Tang

展开摘要

Developing computational models of neural response is crucial for understanding sensory processing and neural computations. Current state-of-the-art neural network methods use temporal filters to handle temporal dependencies, resulting in an **unrealistic and inflexible processing paradigm**. Meanwhile, these methods target **trial-averaged firing rates** and fail to capture important features in spike trains. This work presents the temporal conditioning spiking latent variable models (***TeCoS-LVM***) to simulate the neural response to natural visual stimuli. We use spiking neurons to produce spike outputs that directly match the recorded trains. This approach helps to avoid losing information embedded in the original spike trains. We exclude the temporal dimension from the model parameter space and introduce a temporal conditioning operation to allow the model to adaptively explore and exploit temporal dependencies in stimuli sequences in a **natural paradigm**. We show that TeCoS-LVM models can produce more realistic spike activities and accurately fit spike statistics than powerful alternatives. Additionally, learned TeCoS-LVM models can generalize well to longer time scales. Overall, while remaining computationally tractable, our model effectively captures key features of neural coding systems. It thus provides a useful tool for building accurate predictive computational accounts for various sensory perception circuits.

Poster
Effective Human-AI Teams via Learned Natural Language Rules and Onboarding

Hussein Mozannar, Jimin J Lee, Dennis Wei, Prasanna Sattigeri, Subhro Das, David Sontag

展开摘要

People are relying on AI agents to assist them with various tasks. The human must know when to rely on the agent, collaborate with the agent, or ignore its suggestions. In this work, we propose to learn rules grounded in data regions and described in natural language that illustrate how the human should collaborate with the AI. Our novel region discovery algorithm finds local regions in the data as neighborhoods in an embedding space that corrects the human prior. Each region is then described using an iterative and contrastive procedure where a large language model describes the region. We then teach these rules to the human via an onboarding stage. Through user studies on object detection and question-answering tasks, we show that our method can lead to more accurate human-AI teams. We also evaluate our region discovery and description algorithms separately.

Spotlight
A Path to Simpler Models Starts With Noise

Lesia Semenova, Harry Chen, Ronald Parr, Cynthia Rudin

展开摘要

The Rashomon set is the set of models that perform approximately equally well on a given dataset, and the Rashomon ratio is the fraction of all models in a given hypothesis space that are in the Rashomon set. Rashomon ratios are often large for tabular datasets in criminal justice, healthcare, lending, education, and in other areas, which has practical implications about whether simpler models can attain the same level of accuracy as more complex models. An open question is why Rashomon ratios often tend to be large. In this work, we propose and study a mechanism of the data generation process, coupled with choices usually made by the analyst during the learning process, that determines the size of the Rashomon ratio. Specifically, we demonstrate that noisier datasets lead to larger Rashomon ratios through the way that practitioners train models. Additionally, we introduce a measure called pattern diversity, which captures the average difference in predictions between distinct classification patterns in the Rashomon set, and motivate why it tends to increase with label noise. Our results explain a key aspect of why simpler models often tend to perform as well as black box models on complex, noisier datasets.

Poster
$k$-Means Clustering with Distance-Based Privacy

Alessandro Epasto, Vahab Mirrokni, Shyam Narayanan, Peilin Zhong

展开摘要

In this paper, we initiate the study of Euclidean clustering with Distance-based privacy. Distance-based privacy is motivated by the fact that it is often only needed to protect the privacy of exact, rather than approximate, locations. We provide constant-approximate algorithms for $k$-means and $k$-median clustering, with additive error depending only on the attacker's precision bound $\rho$, rather than the radius $\Lambda$ of the space. In addition, we empirically demonstrate that our algorithm performs significantly better than previous differentially private clustering algorithms, as well as naive distance-based private clustering baselines.

Poster
Pgx: Hardware-Accelerated Parallel Game Simulators for Reinforcement Learning

Sotetsu Koyamada, Shinri Okano, Soichiro Nishimori, Yu Murata, Keigo Habara, Haruka Kita, Shin Ishii

展开摘要

We propose Pgx, a suite of board game reinforcement learning (RL) environments written in JAX and optimized for GPU/TPU accelerators. By leveraging JAX's auto-vectorization and parallelization over accelerators, Pgx can efficiently scale to thousands of simultaneous simulations over accelerators. In our experiments on a DGX-A100 workstation, we discovered that Pgx can simulate RL environments 10-100x faster than existing implementations available in Python. Pgx includes RL environments commonly used as benchmarks in RL research, such as backgammon, chess, shogi, and Go. Additionally, Pgx offers miniature game sets and baseline models to facilitate rapid research cycles. We demonstrate the efficient training of the Gumbel AlphaZero algorithm with Pgx environments. Overall, Pgx provides high-performance environment simulators for researchers to accelerate their RL experiments. Pgx is available at https://github.com/sotetsuk/pgx.

Poster
Guiding Large Language Models via Directional Stimulus Prompting

Zekun Li, Baolin Peng, Pengcheng He, Michel Galley, Jianfeng Gao, Xifeng Yan

展开摘要

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) towards specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We evaluate our method across various tasks, including summarization, dialogue response generation, and chain-of-thought reasoning. Our experiments indicate a consistent improvement in the performance of LLMs such as ChatGPT, Codex, and InstructGPT on these supervised tasks with minimal labeled data. Remarkably, by utilizing merely 80 dialogues from the MultiWOZ dataset, our approach boosts ChatGPT's performance by a relative 41.4%, achieving or exceeding the performance of some fully supervised state-of-the-art models. Moreover, the instance-specific chain-of-thought prompt generated through our method enhances InstructGPT's reasoning accuracy, outperforming both generalized human-crafted prompts and those generated through automatic prompt engineering. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

Poster
UP-NeRF: Unconstrained Pose Prior-Free Neural Radiance Field

Injae Kim, Minhyuk Choi, Hyunwoo J. Kim

展开摘要

Neural Radiance Field (NeRF) has enabled novel view synthesis with high fidelity given images and camera poses. Subsequent works even succeeded in eliminating the necessity of pose priors by jointly optimizing NeRF and camera pose. However, these works are limited to relatively simple settings such as photometrically consistent and occluder-free image collections or a sequence of images from a video. So they have difficulty handling unconstrained images with varying illumination and transient occluders. In this paper, we propose **UP-NeRF** (**U**nconstrained **P**ose-prior-free **Ne**ural **R**adiance **F**ields) to optimize NeRF with unconstrained image collections without camera pose prior. We tackle these challenges with surrogate tasks that optimize color-insensitive feature fields and a separate module for transient occluders to block their influence on pose estimation. In addition, we introduce a candidate head to enable more robust pose estimation and transient-aware depth supervision to minimize the effect of incorrect prior. Our experiments verify the superior performance of our method compared to the baselines including BARF and its variants in a challenging internet photo collection, *Phototourism dataset*. The code of UP-NeRF is available at https://github.com/mlvlab/UP-NeRF.

Poster
Bayesian Optimisation of Functions on Graphs

Xingchen Wan, Pierre Osselin, Henry Kenlay, Binxin Ru, Michael A Osborne, Xiaowen Dong

展开摘要

The increasing availability of graph-structured data motivates the task of optimising over functions defined on the node set of graphs. Traditional graph search algorithms can be applied in this case, but they may be sample-inefficient and do not make use of information about the function values; on the other hand, Bayesian optimisation is a class of promising black-box solvers with superior sample efficiency, but it has scarcely been applied to such novel setups. To fill this gap, we propose a novel Bayesian optimisation framework that optimises over functions defined on generic, large-scale and potentially unknown graphs. Through the learning of suitable kernels on graphs, our framework has the advantage of adapting to the behaviour of the target function. The local modelling approach further guarantees the efficiency of our method. Extensive experiments on both synthetic and real-world graphs demonstrate the effectiveness of the proposed optimisation framework.

Poster
Polynomially Over-Parameterized Convolutional Neural Networks Contain Structured Strong Winning Lottery Tickets

Arthur da Cunha, Francesco D'Amore, Emanuele Natale

展开摘要

The Strong Lottery Ticket Hypothesis (SLTH) states that randomly-initialised neural networks likely contain subnetworks that perform well without any training. Although unstructured pruning has been extensively studied in this context, its structured counterpart, which can deliver significant computational and memory efficiency gains, has been largely unexplored. One of the main reasons for this gap is the limitations of the underlying mathematical tools used in formal analyses of the SLTH. In this paper, we overcome these limitations: we leverage recent advances in the multidimensional generalisation of the Random Subset-Sum Problem and obtain a variant that admits the stochastic dependencies that arise when addressing structured pruning in the SLTH. We apply this result to prove, for a wide class of random Convolutional Neural Networks, the existence of structured subnetworks that can approximate any sufficiently smaller network. This result provides the first sub-exponential bound around the SLTH for structured pruning, opening up new avenues for further research on the hypothesis and contributing to the understanding of the role of over-parameterization in deep learning.

Poster
Language Is Not All You Need: Aligning Perception with Language Models

Shaohan Huang, Li Dong, Wenhui Wang, Yaru Hao, Saksham Singhal, Shuming Ma, Tengchao Lv, Lei Cui, Owais Khan Mohammed, Barun Patra, Qiang Liu, Kriti Aggarwal, Zewen Chi, Johan Bjorck, Vishrav Chaudhary, Subhojit Som, Xia Song, Furu Wei

展开摘要

A big convergence of language, multimodal perception, action, and world modeling is a key step toward artificial general intelligence. In this work, we introduce KOSMOS-1, a Multimodal Large Language Model (MLLM) that can perceive general modalities, learn in context (i.e., few-shot), and follow instructions (i.e., zero-shot). Specifically, we train KOSMOS-1 from scratch on web-scale multi-modal corpora, including arbitrarily interleaved text and images, image-caption pairs, and text data. We evaluate various settings, including zero-shot, few-shot, and multimodal chain-of-thought prompting, on a wide range of tasks without any gradient updates or finetuning. Experimental results show that KOSMOS-1 achieves impressive performance on (i) language understanding, generation, and even OCR-free NLP (directly fed with document images), (ii) perception-language tasks, including multimodal dialogue, image captioning, visual question answering, and (iii) vision tasks, such as image recognition with descriptions (specifying classification via text instructions). We also show that MLLMs can benefit from cross-modal transfer, i.e., transfer knowledge from language to multimodal, and from multimodal to language. In addition, we introduce a dataset of Raven IQ test, which diagnoses the nonverbal reasoning capability of MLLMs.

Poster
Extending the Design Space of Graph Neural Networks by Rethinking Folklore Weisfeiler-Lehman

Jiarui Feng, Lecheng Kong, Hao Liu, Dacheng Tao, Fuhai Li, Muhan Zhang, Yixin Chen

展开摘要

Message passing neural networks (MPNNs) have emerged as the most popular framework of graph neural networks (GNNs) in recent years. However, their expressive power is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Some works are inspired by $k$-WL/FWL (Folklore WL) and design the corresponding neural versions. Despite the high expressive power, there are serious limitations in this line of research. In particular, (1) $k$-WL/FWL requires at least $O(n^k)$ space complexity, which is impractical for large graphs even when $k=3$; (2) The design space of $k$-WL/FWL is rigid, with the only adjustable hyper-parameter being $k$. To tackle the first limitation, we propose an extension, $(k, t)$-FWL. We theoretically prove that even if we fix the space complexity to $O(n^k)$ (for any $k \geq 2$) in $(k, t)$-FWL, we can construct an expressiveness hierarchy up to solving the graph isomorphism problem. To tackle the second problem, we propose $k$-FWL+, which considers any equivariant set as neighbors instead of all nodes, thereby greatly expanding the design space of $k$-FWL. Combining these two modifications results in a flexible and powerful framework $(k, t)$-FWL+. We demonstrate $(k, t)$-FWL+ can implement most existing models with matching expressiveness. We then introduce an instance of $(k,t)$-FWL+ called Neighborhood$^2$-FWL (N$^2$-FWL), which is practically and theoretically sound. We prove that N$^2$-FWL is no less powerful than 3-WL, and can encode many substructures while only requiring $O(n^2)$ space. Finally, we design its neural version named **N$^2$-GNN** and evaluate its performance on various tasks. N$^2$-GNN achieves record-breaking results on ZINC-Subset (**0.059**), outperforming previous SOTA results by 10.6\%. Moreover, N$^2$-GNN achieves new SOTA results on the BREC dataset (**71.8\%**) among all existing high-expressive GNN methods.

Poster
Textually Pretrained Speech Language Models

Michael Hassid, Tal Remez, Tu Anh Nguyen, Itai Gat, Alexis Conneau, Felix Kreuk, Jade Copet, Alexandre Défossez, Gabriel Synnaeve, Emmanuel Dupoux, Roy Schwartz, Yossi Adi

展开摘要

Speech language models (SpeechLMs) process and generate acoustic data only, without textual supervision. In this work, we propose TWIST, a method for training SpeechLMs using a warm-start from a pretrained textual language models. We show using both automatic and human evaluations that TWIST outperforms a cold-start SpeechLM across the board. We empirically analyze the effect of different model design choices such as the speech tokenizer, the pretrained textual model, and the dataset size. We find that model and dataset scale both play an important role in constructing better-performing SpeechLMs. Based on our observations, we present the largest (to the best of our knowledge) SpeechLM both in terms of number of parameters and training data. We additionally introduce two spoken versions of the StoryCloze textual benchmark to further improve model evaluation and advance future research in the field. We make speech samples, code and models publicly available.

Poster
Approximate Heavy Tails in Offline (Multi-Pass) Stochastic Gradient Descent

Krunoslav Lehman Pavasovic, Alain Durmus, Umut Simsekli

展开摘要

A recent line of empirical studies has demonstrated that SGD might exhibit a heavy-tailed behavior in practical settings, and the heaviness of the tails might correlate with the overall performance. In this paper, we investigate the emergence of such heavy tails. Previous works on this problem only considered, up to our knowledge, online (also called single-pass) SGD, in which the emergence of heavy tails in theoretical findings is contingent upon access to an infinite amount of data. Hence, the underlying mechanism generating the reported heavy-tailed behavior in practical settings, where the amount of training data is finite, is still not well-understood. Our contribution aims to fill this gap. In particular, we show that the stationary distribution of offline (also called multi-pass) SGD exhibits ‘approximate’ power-law tails and the approximation error is controlled by how fast the empirical distribution of the training data converges to the true underlying data distribution in the Wasserstein metric. Our main takeaway is that, as the number of data points increases, offline SGD will behave increasingly ‘power-law-like’. To achieve this result, we first prove nonasymptotic Wasserstein convergence bounds for offline SGD to online SGD as the number of data points increases, which can be interesting on their own. Finally, we illustrate our theory on various experiments conducted on synthetic data and neural networks.

Spotlight