NeurIPS 2023 论文列表

Representations learned by pre-training a neural network on a large dataset are increasingly used successfully to perform a variety of downstream tasks. In this work, we take a closer look at how features are encoded in such pre-trained representations. We find that learned representations in a given layer exhibit a degree of diffuse redundancy, ie, any randomly chosen subset of neurons in the layer that is larger than a threshold size shares a large degree of similarity with the full layer and is able to perform similarly as the whole layer on a variety of downstream tasks. For example, a linear probe trained on $20\%$ of randomly picked neurons from the penultimate layer of a ResNet50 pre-trained on ImageNet1k achieves an accuracy within $5\%$ of a linear probe trained on the full layer of neurons for downstream CIFAR10 classification. We conduct experiments on different neural architectures (including CNNs and Transformers) pre-trained on both ImageNet1k and ImageNet21k and evaluate a variety of downstream tasks taken from the VTAB benchmark. We find that the loss \& dataset used during pre-training largely govern the degree of diffuse redundancy and the "critical mass" of neurons needed often depends on the downstream task, suggesting that there is a task-inherent redundancy-performance Pareto frontier. Our findings shed light on the nature of representations learned by pre-trained deep neural networks and suggest that entire layers might not be necessary to perform many downstream tasks. We investigate the potential for exploiting this redundancy to achieve efficient generalization for downstream tasks and also draw caution to certain possible unintended consequences. Our code is available at \url{https://github.com/nvedant07/diffused-redundancy}.

Overparameterized neural networks (NNs) are observed to generalize well even when trained to perfectly fit noisy data. This phenomenon motivated a large body of work on "benign overfitting", where interpolating predictors achieve near-optimal performance. Recently, it was conjectured and empirically observed that the behavior of NNs is often better described as "tempered overfitting", where the performance is non-optimal yet also non-trivial, and degrades as a function of the noise level. However, a theoretical justification of this claim for non-linear NNs has been lacking so far. In this work, we provide several results that aim at bridging these complementing views. We study a simple classification setting with 2-layer ReLU NNs, and prove that under various assumptions, the type of overfitting transitions from tempered in the extreme case of one-dimensional data, to benign in high dimensions. Thus, we show that the input dimension has a crucial role on the overfitting profile in this setting, which we also validate empirically for intermediate dimensions. Overall, our results shed light on the intricate connections between the dimension, sample size, architecture and training algorithm on the one hand, and the type of resulting overfitting on the other hand.

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this temporal flexibility often comes with a high sensitivity to noise, whereas medical problems often present high noise and limited data. Moreover, medical dosing models must generalize reliably over individual patients and changing treatment policies. To address these challenges, we introduce the Neural Eigen Stochastic Differential Equation algorithm (NESDE). NESDE provides individualized modeling (using a hypernetwork over patient-level parameters); generalization to new treatment policies (using decoupled control); tunable expressiveness according to the noise level (using piecewise linearity); and fast, continuous, closed-form prediction (using spectral representation). We demonstrate the robustness of NESDE in both synthetic and real medical problems, and use the learned dynamics to publish simulated medical gym environments.

We aim to deepen the theoretical understanding of Graph Neural Networks (GNNs) on large graphs, with a focus on their expressive power. Existing analyses relate this notion to the graph isomorphism problem, which is mostly relevant for graphs of small sizes, or studied graph classification or regression tasks, while prediction tasks on \emph{nodes} are far more relevant on large graphs. Recently, several works showed that, on very general random graphs models, GNNs converge to certains functions as the number of nodes grows. In this paper, we provide a more complete and intuitive description of the function space generated by equivariant GNNs for node-tasks, through general notions of convergence that encompass several previous examples. We emphasize the role of input node features, and study the impact of \emph{node Positional Encodings} (PEs), a recent line of work that has been shown to yield state-of-the-art results in practice. Through the study of several examples of PEs on large random graphs, we extend previously known universality results to significantly more general models. Our theoretical results hint at some normalization tricks, which is shown numerically to have a positive impact on GNN generalization on synthetic and real data. Our proofs contain new concentration inequalities of independent interest.

We study benign overfitting in two-layer ReLU networks trained using gradient descent and hinge loss on noisy data for binary classification. In particular, we consider linearly separable data for which a relatively small proportion of labels are corrupted or flipped. We identify conditions on the margin of the clean data that give rise to three distinct training outcomes: benign overfitting, in which zero loss is achieved and with high probability test data is classified correctly; overfitting, in which zero loss is achieved but test data is misclassified with probability lower bounded by a constant; and non-overfitting, in which clean points, but not corrupt points, achieve zero loss and again with high probability test data is classified correctly. Our analysis provides a fine-grained description of the dynamics of neurons throughout training and reveals two distinct phases: in the first phase clean points achieve close to zero loss, in the second phase clean points oscillate on the boundary of zero loss while corrupt points either converge towards zero loss or are eventually zeroed by the network. We prove these results using a combinatorial approach that involves bounding the number of clean versus corrupt updates during these phases of training.

We introduce Markov Neural Processes (MNPs), a new class of Stochastic Processes (SPs) which are constructed by stacking sequences of neural parameterised Markov transition operators in function space. We prove that these Markov transition operators can preserve the exchangeability and consistency of SPs. Therefore, the proposed iterative construction adds substantial flexibility and expressivity to the original framework of Neural Processes (NPs) without compromising consistency or adding restrictions. Our experiments demonstrate clear advantages of MNPs over baseline models on a variety of tasks.

Neural ordinary differential equations (ODEs) are widely recognized as the standard for modeling physical mechanisms, which help to perform approximate inference in unknown physical or biological environments. In partially observable (PO) environments, how to infer unseen information from raw observations puzzled the agents. By using a recurrent policy with a compact context, context-based reinforcement learning provides a flexible way to extract unobservable information from historical transitions. To help the agent extract more dynamics-related information, we present a novel ODE-based recurrent model combines with model-free reinforcement learning (RL) framework to solve partially observable Markov decision processes (POMDPs). We experimentally demonstrate the efficacy of our methods across various PO continuous control and meta-RL tasks. Furthermore, our experiments illustrate that our method is robust against irregular observations, owing to the ability of ODEs to model irregularly-sampled time series.

We study the effect of width on the dynamics of feature-learning neural networks across a variety of architectures and datasets. Early in training, wide neural networks trained on online data have not only identical loss curves but also agree in their point-wise test predictions throughout training. For simple tasks such as CIFAR-5m this holds throughout training for networks of realistic widths. We also show that structural properties of the models, including internal representations, preactivation distributions, edge of stability phenomena, and large learning rate effects are consistent across large widths. This motivates the hypothesis that phenomena seen in realistic models can be captured by infinite-width, feature-learning limits. For harder tasks (such as ImageNet and language modeling), and later training times, finite-width deviations grow systematically. Two distinct effects cause these deviations across widths. First, the network output has an initialization-dependent variance scaling inversely with width, which can be removed by ensembling networks. We observe, however, that ensembles of narrower networks perform worse than a single wide network. We call this the bias of narrower width. We conclude with a spectral perspective on the origin of this finite-width bias.

This paper considers a class of reinforcement learning problems, which involve systems with two types of states: stochastic and pseudo-stochastic. In such systems, stochastic states follow a stochastic transition kernel while the transitions of pseudo-stochastic states are deterministic {\em given} the stochastic states/transitions. We refer to such systems as mixed systems, which are widely used in various applications, including Manufacturing systems, communication networks, and queueing networks. We propose a sample-efficient RL method that accelerates learning by generating augmented data samples. The proposed algorithm is data-driven (model-free), but it learns the policy from data samples from both real and augmented samples. This method significantly improves learning by reducing the sample complexity such that the dataset only needs to have sufficient coverage of the stochastic states. We analyze the sample complexity of the proposed method under Fitted Q Iteration (FQI) and demonstrate that the optimality gap decreases as $O\left(\sqrt{\frac{1}{n}}+\sqrt{\frac{1}{m}}\right),$ where $n$ represents the number of real samples, and $m$ is the number of augmented samples per real sample. It is important to note that without augmented samples, the optimality gap is $O(1)$ due to the insufficient data coverage of the pseudo-stochastic states. Our experimental results on multiple queueing network applications confirm that the proposed method indeed significantly accelerates both deep Q-learning and deep policy gradient.

Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the structural knowledge within the sparsely observed tensor entries. To overcome these limitations and to better capture the underlying temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to estimate dynamic embeddings for the entities in each tensor mode. Specifically, based on the observed tensor entries, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model can capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the entry value as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both simulation studies and real-world applications. The code is available at https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes.

Federated Learning (FL) is a promising research paradigm that enables the collaborative training of machine learning models among various parties without the need for sensitive information exchange. Nonetheless, retaining data in individual clients introduces fundamental challenges to achieving performance on par with centrally trained models. Our study provides an extensive review of federated learning applied to visual recognition. It underscores the critical role of thoughtful architectural design choices in achieving optimal performance, a factor often neglected in the FL literature. Many existing FL solutions are tested on shallow or simple networks, which may not accurately reflect real-world applications. This practice restricts the transferability of research findings to large-scale visual recognition models. Through an in-depth analysis of diverse cutting-edge architectures such as convolutional neural networks, transformers, and MLP-mixers, we experimentally demonstrate that architectural choices can substantially enhance FL systems' performance, particularly when handling heterogeneous data. We study visual recognition models from five different architectural families on four challenging FL datasets. We also re-investigate the inferior performance convolution-based architectures in the FL setting and analyze the influence of normalization layers on the FL performance. Our findings emphasize the importance of architectural design for computer vision tasks in practical scenarios, effectively narrowing the performance gap between federated and centralized learning.

It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deep learning vision models suffer in a variety of settings that humans capably handle. In light of these phenomena, here we introduce another, orthogonal perspective studying the human-machine vision gap. We revisit the task of recovering images under degradation, first introduced over 30 years ago in the Recognition-by-Components theory of human vision. Specifically, we study the performance and behavior of neural networks on the seemingly simple task of classifying regular polygons at varying orders of degradation along their perimeters. To this end, we implement the Automated Shape Recoverability Test for rapidly generating large-scale datasets of perimeter-degraded regular polygons, modernizing the historically manual creation of image recoverability experiments. We then investigate the capacity of neural networks to recognize and recover such degraded shapes when initialized with different priors. Ultimately, we find that neural networks’ behavior on this simple task conflicts with human behavior, raising a fundamental question of the robustness and learning capabilities of modern computer vision models

To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the training process itself (e.g., min-max optimization, constrained learning, or regularization). These approaches, however, might not be effective at increasing the margin in the input (feature) space. In this paper, we propose a differentiable regularizer that is a lower bound on the distance of the data points to the classification boundary. The proposed regularizer requires knowledge of the model's Lipschitz constant along certain directions. To this end, we develop a scalable method for calculating guaranteed differentiable upper bounds on the Lipschitz constant of neural networks accurately and efficiently. The relative accuracy of the bounds prevents excessive regularization and allows for more direct manipulation of the decision boundary. Furthermore, our Lipschitz bounding algorithm exploits the monotonicity and Lipschitz continuity of the activation layers, and the resulting bounds can be used to design new layers with controllable bounds on their Lipschitz constant. Experiments on the MNIST, CIFAR-10, and Tiny-ImageNet data sets verify that our proposed algorithm obtains competitively improved results compared to the state-of-the-art.

In many information processing systems, it may be desirable to ensure that any change of the input, whether by shifting or scaling, results in a corresponding change in the system response. While deep neural networks are gradually replacing all traditional automatic processing methods, they surprisingly do not guarantee such normalization-equivariance (scale + shift) property, which can be detrimental in many applications. To address this issue, we propose a methodology for adapting existing neural networks so that normalization-equivariance holds by design. Our main claim is that not only ordinary convolutional layers, but also all activation functions, including the ReLU (rectified linear unit), which are applied element-wise to the pre-activated neurons, should be completely removed from neural networks and replaced by better conditioned alternatives. To this end, we introduce affine-constrained convolutions and channel-wise sort pooling layers as surrogates and show that these two architectural modifications do preserve normalization-equivariance without loss of performance. Experimental results in image denoising show that normalization-equivariant neural networks, in addition to their better conditioning, also provide much better generalization across noise levels.

Simultaneous behavioral and electrophysiological recordings call for new methods to reveal the interactions between neural activity and behavior. A milestone would be an interpretable model of the co-variability of spiking activity and behavior across trials. Here, we model a mouse cortical sensory-motor pathway in a tactile detection task reported by licking with a large recurrent spiking neural network (RSNN), fitted to the recordings via gradient-based optimization. We focus specifically on the difficulty to match the trial-to-trial variability in the data. Our solution relies on optimal transport to define a distance between the distributions of generated and recorded trials. The technique is applied to artificial data and neural recordings covering six cortical areas. We find that the resulting RSNN can generate realistic cortical activity and predict jaw movements across the main modes of trial-to-trial variability. Our analysis also identifies an unexpected mode of variability in the data corresponding to task-irrelevant movements of the mouse.

Systems of interacting objects often evolve under the influence of underlying field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions --which are SE(3) equivariant and depend on relative states-- from external global field effects --which depend on absolute states. We model the interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

This paper advocates a new paradigm Personalized Empirical Risk Minimization (PERM) to facilitate learning from heterogeneous data sources without imposing stringent constraints on computational resources shared by participating devices. In PERM, we aim at learning a distinct model for each client by personalizing the aggregation of local empirical losses by effectively estimating the statistical discrepancy among data distributions, which entails optimal statistical accuracy for all local distributions and overcomes the data heterogeneity issue. To learn personalized models at scale, we propose a distributed algorithm that replaces the standard model averaging with model shuffling to simultaneously optimize PERM objectives for all devices. This also allows to learn distinct model architectures (e.g., neural networks with different number of parameters) for different clients, thus confining to underlying memory and compute resources of individual clients. We rigorously analyze the convergence of proposed algorithm and conduct experiments that corroborates the effectiveness of proposed paradigm.

Variance-Invariance-Covariance Regularization (VICReg) is a self-supervised learning (SSL) method that has shown promising results on a variety of tasks. However, the fundamental mechanisms underlying VICReg remain unexplored. In this paper, we present an information-theoretic perspective on the VICReg objective. We begin by deriving information-theoretic quantities for deterministic networks as an alternative to unrealistic stochastic network assumptions. We then relate the optimization of the VICReg objective to mutual information optimization, highlighting underlying assumptions and facilitating a constructive comparison with other SSL algorithms and derive a generalization bound for VICReg, revealing its inherent advantages for downstream tasks. Building on these results, we introduce a family of SSL methods derived from information-theoretic principles that outperform existing SSL techniques.