NeurIPS 2023 论文列表

In this paper, we derive norm-based generalization bounds for sparse ReLU neural networks, including convolutional neural networks. These bounds differ from previous ones because they consider the sparse structure of the neural network architecture and the norms of the convolutional filters, rather than the norms of the (Toeplitz) matrices associated with the convolutional layers. Theoretically, we demonstrate that these bounds are significantly tighter than standard norm-based generalization bounds. Empirically, they offer relatively tight estimations of generalization for various simple classification problems. Collectively, these findings suggest that the sparsity of the underlying target function and the model's architecture plays a crucial role in the success of deep learning.

In this paper, we present a novel robust framework for low-level vision tasks, including denoising, object removal, frame interpolation, and super-resolution, that does not require any external training data corpus. Our proposed approach directly learns the weights of neural modules by optimizing over the corrupted test sequence, leveraging the spatio-temporal coherence and internal statistics of videos. Furthermore, we introduce a novel spatial pyramid loss that leverages the property of spatio-temporal patch recurrence in a video across the different scales of the video. This loss enhances robustness to unstructured noise in both the spatial and temporal domains. This further results in our framework being highly robust to degradation in input frames and yields state-of-the-art results on downstream tasks such as denoising, object removal, and frame interpolation. To validate the effectiveness of our approach, we conduct qualitative and quantitative evaluations on standard video datasets such as DAVIS, UCF-101, and VIMEO90K-T.

The neural population spiking activity recorded by intracortical brain-computer interfaces (iBCIs) contain rich structure. Current models of such spiking activity are largely prepared for individual experimental contexts, restricting data volume to that collectable within a single session and limiting the effectiveness of deep neural networks (DNNs). The purported challenge in aggregating neural spiking data is the pervasiveness of context-dependent shifts in the neural data distributions. However, large scale unsupervised pretraining by nature spans heterogeneous data, and has proven to be a fundamental recipe for successful representation learning across deep learning. We thus develop Neural Data Transformer 2 (NDT2), a spatiotemporal Transformer for neural spiking activity, and demonstrate that pretraining can leverage motor BCI datasets that span sessions, subjects, and experimental tasks. NDT2 enables rapid adaptation to novel contexts in downstream decoding tasks and opens the path to deployment of pretrained DNNs for iBCI control. Code: https://github.com/joel99/context_general_bci

Sparse training has received an upsurging interest in machine learning due to its tantalizing saving potential for both the entire training process as well as the inference. Dynamic sparse training (DST) as a leading approach can train deep neural networks at high sparsity from scratch to match the performance of their dense counterparts. However, most if not all DST prior arts demonstrate their effectiveness on unstructured sparsity with highly irregular sparse patterns, which receives limited support in common hardware. This limitation hinders the usage of DST in practice. In this paper, we propose Channel-aware dynamic sparse (Chase), that for the first time seamlessly translates the promise of unstructured dynamic sparsity to GPU-friendly channel-level sparsity (not fine-grained N:M or group sparsity) during one end-to-end training process, without any ad-hoc operations. The resulting small sparse networks can be directly accelerated by commodity hardware, without using any particularly sparsity-aware hardware accelerators. This appealing outcome is partially motivated by a hidden phenomenon of dynamic sparsity: off-the-shelf unstructured DST implicitly involves biased parameter reallocation across channels, with a large fraction of channels (up to 60%) being sparser than others. By progressively identifying and removing these channels during training, our approach transfers unstructured sparsity to channel-wise sparsity. Our experimental results demonstrate that Chase achieves 1.7x inference throughput speedup on common GPU devices without compromising accuracy with ResNet-50 on ImageNet. We release our code in https://github.com/luuyin/chase.

Input gradients have a pivotal role in a variety of applications, including adversarial attack algorithms for evaluating model robustness, explainable AI techniques for generating saliency maps, and counterfactual explanations. However, saliency maps generated by traditional neural networks are often noisy and provide limited insights. In this paper, we demonstrate that, on the contrary, the saliency maps of 1-Lipschitz neural networks, learnt with the dual loss of an optimal transportation problem, exhibit desirable XAI properties: They are highly concentrated on the essential parts of the image with low noise, significantly outperforming state-of-the-art explanation approaches across various models and metrics. We also prove that these maps align unprecedentedly well with human explanations on ImageNet. To explain the particularly beneficial properties of the saliency map for such models, we prove this gradient encodes both the direction of the transportation plan and the direction towards the nearest adversarial attack. Following the gradient down to the decision boundary is no longer considered an adversarial attack, but rather a counterfactual explanation that explicitly transports the input from one class to another. Thus, Learning with such a loss jointly optimizes the classification objective and the alignment of the gradient , i.e. the saliency map, to the transportation plan direction. These networks were previously known to be certifiably robust by design, and we demonstrate that they scale well for large problems and models, and are tailored for explainability using a fast and straightforward method.

Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible as functions of their input features than black-box models like deep neural networks. With this capability gap in mind, we study a not-uncommon situation where the input features dichotomize into two groups: explanatory features, which are candidates for inclusion as variables in an interpretable model, and contextual features, which select from the candidate variables and determine their effects. This dichotomy leads us to the contextual lasso, a new statistical estimator that fits a sparse linear model to the explanatory features such that the sparsity pattern and coefficients vary as a function of the contextual features. The fitting process learns this function nonparametrically via a deep neural network. To attain sparse coefficients, we train the network with a novel lasso regularizer in the form of a projection layer that maps the network's output onto the space of $\ell_1$-constrained linear models. An extensive suite of experiments on real and synthetic data suggests that the learned models, which remain highly transparent, can be sparser than the regular lasso without sacrificing the predictive power of a standard deep neural network.

Despite the success of neural-based combinatorial optimization methods for end-to-end heuristic learning, out-of-distribution generalization remains a challenge. In this paper, we present a novel formulation of Combinatorial Optimization Problems (COPs) as Markov Decision Processes (MDPs) that effectively leverages common symmetries of COPs to improve out-of-distribution robustness. Starting from a direct MDP formulation of a constructive method, we introduce a generic way to reduce the state space, based on Bisimulation Quotienting (BQ) in MDPs. Then, for COPs with a recursive nature, we specialize the bisimulation and show how the reduced state exploits the symmetries of these problems and facilitates MDP solving. Our approach is principled and we prove that an optimal policy for the proposed BQ-MDP actually solves the associated COPs. We illustrate our approach on five classical problems: the Euclidean and Asymmetric Traveling Salesman, Capacitated Vehicle Routing, Orienteering and Knapsack Problems. Furthermore, for each problem, we introduce a simple attention-based policy network for the BQ-MDPs, which we train by imitation of (near) optimal solutions of small instances from a single distribution. We obtain new state-of-the-art results for the five COPs on both synthetic and realistic benchmarks. Notably, in contrast to most existing neural approaches, our learned policies show excellent generalization performance to much larger instances than seen during training, without any additional search procedure. Our code is available at: [link](https://github.com/naver/bq-nco).

Gromov-Wasserstein (GW) distance is a powerful tool for comparing and aligning probability distributions supported on different metric spaces. Recently, GW has become the main modeling technique for aligning heterogeneous data for a wide range of graph learning tasks. However, the GW distance is known to be highly sensitive to outliers, which can result in large inaccuracies if the outliers are given the same weight as other samples in the objective function. To mitigate this issue, we introduce a new and robust version of the GW distance called RGW. RGW features optimistically perturbed marginal constraints within a Kullback-Leibler divergence-based ambiguity set. To make the benefits of RGW more accessible in practice, we develop a computationally efficient and theoretically provable procedure using Bregman proximal alternating linearized minimization algorithm. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of RGW on real-world graph learning tasks, such as subgraph matching and partial shape correspondence.

The performance of deep learning models heavily relies on the quality of the training data. Inadequacies in the training data, such as corrupt input or noisy labels, can lead to the failure of model generalization. Recent studies propose repairing the model by identifying the training samples that contribute to the failure and removing their influence from the model. However, it is important to note that the identified data may contain both beneficial and detrimental information. Simply erasing the information of the identified data from the model can have a negative impact on its performance, especially when accurate data is mistakenly identified as detrimental and removed. To overcome this challenge, we propose a novel approach that leverages the knowledge obtained from a retained clean set. Our method first identifies harmful data by utilizing the clean set, then separates the beneficial and detrimental information within the identified data. Finally, we utilize the extracted beneficial information to enhance the model's performance. Through empirical evaluations, we demonstrate that our method outperforms baseline approaches in both identifying harmful data and rectifying model failures. Particularly in scenarios where identification is challenging and a significant amount of benign data is involved, our method improves performance while the baselines deteriorate due to the erroneous removal of beneficial information.

Neural Radiance Fields (NeRF) have become an increasingly popular representation to capture high-quality appearance and shape of scenes and objects. However, learning generalizable NeRF priors over categories of scenes or objects has been challenging due to the high dimensionality of network weight space. To address the limitations of existing work on generalization, multi-view consistency and to improve quality, we propose HyP-NeRF, a latent conditioning method for learning generalizable category-level NeRF priors using hypernetworks. Rather than using hypernetworks to estimate only the weights of a NeRF, we estimate both the weights and the multi-resolution hash encodings resulting in significant quality gains. To improve quality even further, we incorporate a denoise and finetune strategy that denoises images rendered from NeRFs estimated by the hypernetwork and finetunes it while retaining multiview consistency. These improvements enable us to use HyP-NeRF as a generalizable prior for multiple downstream tasks including NeRF reconstruction from single-view or cluttered scenes and text-to-NeRF. We provide qualitative comparisons and evaluate HyP-NeRF on three tasks: generalization, compression, and retrieval, demonstrating our state-of-the-art results.

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that leverages Cartesian tensor representations. By using Cartesian tensor atomic embeddings, feature mixing is simplified through matrix product operations. Furthermore, the cost-effective decomposition of these tensors into rotation group irreducible representations allows for the separate processing of scalars, vectors, and tensors when necessary. Compared to higher-rank spherical tensor models, TensorNet demonstrates state-of-the-art performance with significantly fewer parameters. For small molecule potential energies, this can be achieved even with a single interaction layer. As a result of all these properties, the model's computational cost is substantially decreased. Moreover, the accurate prediction of vector and tensor molecular quantities on top of potential energies and forces is possible. In summary, TensorNet's framework opens up a new space for the design of state-of-the-art equivariant models.

This paper proposes a novel algorithm, Transformative Bayesian Learning (TansBL), which bridges the gap between empirical risk minimization (ERM) and Bayesian learning for neural networks. We compare ERM, which uses gradient descent to optimize, and Bayesian learning with importance sampling for their generalization and computational complexity. We derive the first algorithm-dependent PAC-Bayesian generalization bound for infinitely wide networks based on an exact KL divergence between the trained posterior distribution obtained by infinitesimal step size gradient descent and a Gaussian prior. Moreover, we show how to transform gradient-based optimization into importance sampling by incorporating a weight. While Bayesian learning has better generalization, it suffers from low sampling efficiency. Optimization methods, on the other hand, have good sampling efficiency but poor generalization. Our proposed algorithm TansBL enables a trade-off between generalization and sampling efficiency.

Temporal graphs offer more accurate modeling of many real-world scenarios than static graphs. However, neighbor aggregation, a critical building block of graph networks, for temporal graphs, is currently straightforwardly extended from that of static graphs. It can be computationally expensive when involving all historical neighbors during such aggregation. In practice, typically only a subset of the most recent neighbors are involved. However, such subsampling leads to incomplete and biased neighbor information. To address this limitation, we propose a novel framework for temporal neighbor aggregation that uses the recurrent neural network with node-wise hidden states to integrate information from all historical neighbors for each node to acquire the complete neighbor information. We demonstrate the superior theoretical expressiveness of the proposed framework as well as its state-of-the-art performance in real-world applications. Notably, it achieves a significant +9.4% improvement on averaged precision in a real-world Ecommerce dataset over existing methods on 2-layer models.

As a powerful framework for graph representation learning, Graph Neural Networks (GNNs) have garnered significant attention in recent years. However, to the best of our knowledge, there has been no formal analysis of the logical expressiveness of GNNs as Boolean node classifiers over multi-relational graphs, where each edge carries a specific relation type. In this paper, we investigate $\mathcal{FOC}_2$, a fragment of first-order logic with two variables and counting quantifiers. On the negative side, we demonstrate that the R$^2$-GNN architecture, which extends the local message passing GNN by incorporating global readout, fails to capture $\mathcal{FOC}_2$ classifiers in the general case. Nevertheless, on the positive side, we establish that R$^2$-GNNs models are equivalent to $\mathcal{FOC}_2$ classifiers under certain restricted yet reasonable scenarios. To address the limitations of R$^2$-GNNs regarding expressiveness, we propose a simple graph transformation technique, akin to a preprocessing step, which can be executed in linear time. This transformation enables R$^2$-GNNs to effectively capture any $\mathcal{FOC}_2$ classifiers when applied to the "transformed" input graph. Moreover, we extend our analysis of expressiveness and graph transformation to temporal graphs, exploring several temporal GNN architectures and providing an expressiveness hierarchy for them. To validate our findings, we implement R$^2$-GNNs and the graph transformation technique and conduct empirical tests in node classification tasks against various well-known GNN architectures that support multi-relational or temporal graphs. Our experimental results consistently demonstrate that R$^2$-GNN with the graph transformation outperforms the baseline methods on both synthetic and real-world datasets

While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy. However, finding Lyapunov functions for general nonlinear systems is a challenging task. To address this challenge, several methods have been proposed that represent Lyapunov functions using neural networks. However, such approaches either focus on continuous-time systems, or highly restricted classes of nonlinear dynamics. We propose the first approach for learning neural Lyapunov control in a broad class of discrete-time systems. Three key ingredients enable us to effectively learn provably stable control policies. The first is a novel mixed-integer linear programming approach for verifying the discrete-time Lyapunov stability conditions, leveraging the particular structure of these conditions. The second is a novel approach for computing verified sublevel sets. The third is a heuristic gradient-based method for quickly finding counterexamples to significantly speed up Lyapunov function learning. Our experiments on four standard benchmarks demonstrate that our approach significantly outperforms state-of-the-art baselines. For example, on the path tracking benchmark, we outperform recent neural Lyapunov control baselines by an order of magnitude in both running time and the size of the region of attraction, and on two of the four benchmarks (cartpole and PVTOL), ours is the first automated approach to return a provably stable controller. Our code is available at: https://github.com/jlwu002/nlc_discrete.

We systematically analyze optimization dynamics in deep neural networks (DNNs) trained with stochastic gradient descent (SGD) and study the effect of learning rate $\eta$, depth $d$, and width $w$ of the neural network. By analyzing the maximum eigenvalue $\lambda^H_t$ of the Hessian of the loss, which is a measure of sharpness of the loss landscape, we find that the dynamics can show four distinct regimes: (i) an early time transient regime, (ii) an intermediate saturation regime, (iii) a progressive sharpening regime, and (iv) a late time "edge of stability" regime. The early and intermediate regimes (i) and (ii) exhibit a rich phase diagram depending on $\eta \equiv c / \lambda_0^H $, $d$, and $w$. We identify several critical values of $c$, which separate qualitatively distinct phenomena in the early time dynamics of training loss and sharpness. Notably, we discover the opening up of a "sharpness reduction" phase, where sharpness decreases at early times, as $d$ and $ 1/w$ are increased.

Modern predictive models are often deployed to environments in which computational budgets are dynamic. Anytime algorithms are well-suited to such environments as, at any point during computation, they can output a prediction whose quality is a function of computation time. Early-exit neural networks have garnered attention in the context of anytime computation due to their capability to provide intermediate predictions at various stages throughout the network. However, we demonstrate that current early-exit networks are not directly applicable to anytime settings, as the quality of predictions for individual data points is not guaranteed to improve with longer computation. To address this shortcoming, we propose an elegant post-hoc modification, based on the Product-of-Experts, that encourages an early-exit network to become gradually confident. This gives our deep models the property of *conditional monotonicity* in the prediction quality---an essential building block towards truly anytime predictive modeling using early-exit architectures. Our empirical results on standard image-classification tasks demonstrate that such behaviors can be achieved while preserving competitive accuracy on average.

In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, *the first* deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at [https://miralab-ustc.github.io/L2O-G2MILP](https://miralab-ustc.github.io/L2O-G2MILP).

Flexibly quantifying both irreducible aleatoric and model-dependent epistemic uncertainties plays an important role for complex regression problems. While deep neural networks in principle can provide this flexibility and learn heteroscedastic aleatoric uncertainties through non-linear functions, recent works highlight that maximizing the log likelihood objective parameterized by mean and variance can lead to compromised mean fits since the gradient are scaled by the predictive variance, and propose adjustments in line with this premise. We instead propose to use the natural parametrization of the Gaussian, which has been shown to be more stable for heteroscedastic regression based on non-linear feature maps and Gaussian processes. Further, we emphasize the significance of principled regularization of the network parameters and prediction. We therefore propose an efficient Laplace approximation for heteroscedastic neural networks that allows automatic regularization through empirical Bayes and provides epistemic uncertainties, both of which improve generalization. We showcase on a range of regression problems—including a new heteroscedastic image regression benchmark—that our methods are scalable, improve over previous approaches for heteroscedastic regression, and provide epistemic uncertainty without requiring hyperparameter tuning.