NeurIPS 2023 论文列表

This work studies the evaluation of explaining graph neural networks (GNNs), which is crucial to the credibility of post-hoc explainability in practical usage. Conventional evaluation metrics, and even explanation methods -- which mainly follow the paradigm of feeding the explanatory subgraph and measuring output difference -- always suffer from the notorious out-of-distribution (OOD) issue. In this work, we endeavor to confront the issue by introducing a novel evaluation metric, termed **O**OD-resistant **A**dversarial **R**obustness (OAR). Specifically, we draw inspiration from the notion of adversarial robustness and evaluate post-hoc explanation subgraphs by calculating their robustness under attack. On top of that, an elaborate OOD reweighting block is inserted into the pipeline to confine the evaluation process to the original data distribution. For applications involving large datasets, we further devise a **Sim**plified version of **OAR** (SimOAR), which achieves a significant improvement in computational efficiency at the cost of a small amount of performance. Extensive empirical studies validate the effectiveness of our OAR and SimOAR.

Neural Architecture Search (NAS) has emerged as a favoured method for unearthing effective neural architectures. Recent development of large models has intensified the demand for faster search speeds and more accurate search results. However, designing large models by NAS is challenging due to the dramatical increase of search space and the associated huge performance evaluation cost. Consider a typical modular search space widely used in NAS, in which a neural architecture consists of $m$ block nodes and a block node has $n$ alternative blocks. Facing the space containing $n^m$ candidate networks, existing NAS methods attempt to find the best one by searching and evaluating candidate networks directly. Different from the general strategy that takes architecture search as a whole problem, we propose a novel divide-and-conquer strategy by making use of the modular nature of the search space. Here, we introduce MathNAS, a general NAS framework based on mathematical programming. In MathNAS, the performances of all possible building blocks in the search space are calculated first, and then the performance of a network is directly predicted based on the performances of its building blocks. Although estimating block performances involves network training, just as what happens for network performance evaluation in existing NAS methods, predicting network performance is completely training-free and thus extremely fast. In contrast to the $n^m$ candidate networks to evaluate in existing NAS methods, which requires training and a formidable computational burden, there are only $m*n$ possible blocks to handle in MathNAS. Therefore, our approach effectively reduces the complexity of network performance evaluation. The superiority of MathNAS is validated on multiple large-scale CV and NLP benchmark datasets. Notably on ImageNet-1k, MathNAS achieves 82.5\% top-1 accuracy, 1.2\% and 0.96\% higher than Swin-T and LeViT-256, respectively. In addition, when deployed on mobile device, MathNAS achieves real-time search and dynamic network switching within 1s (0.4s on TX2 GPU), surpassing baseline dynamic networks in on-device performance.

Understanding the learning process of artificial neural networks requires clarifying the structure of the parameter space within which learning takes place. A neural network parameter's functional equivalence class is the set of parameters implementing the same input--output function. For many architectures, almost all parameters have a simple and well-documented functional equivalence class. However, there is also a vanishing minority of reducible parameters, with richer functional equivalence classes caused by redundancies among the network's units. In this paper, we give an algorithmic characterisation of unit redundancies and reducible functional equivalence classes for a single-hidden-layer hyperbolic tangent architecture. We show that such functional equivalence classes are piecewise-linear path-connected sets, and that for parameters with a majority of redundant units, the sets have a diameter of at most 7 linear segments.

Graph Neural Networks (GNNs) have proven to be highly effective in solving real-world learning problems that involve graph-structured data. However, GNNs can also inadvertently expose sensitive user information and interactions through their model predictions. To address these privacy concerns, Differential Privacy (DP) protocols are employed to control the trade-off between provable privacy protection and model utility. Applying standard DP approaches to GNNs directly is not advisable due to two main reasons. First, the prediction of node labels, which relies on neighboring node attributes through graph convolutions, can lead to privacy leakage. Second, in practical applications, the privacy requirements for node attributes and graph topology may differ. In the latter setting, existing DP-GNN models fail to provide multigranular trade-offs between graph topology privacy, node attribute privacy, and GNN utility. To address both limitations, we propose a new framework termed Graph Differential Privacy (GDP), specifically tailored to graph learning. GDP ensures both provably private model parameters as well as private predictions. Additionally, we describe a novel unified notion of graph dataset adjacency to analyze the properties of GDP for different levels of graph topology privacy. Our findings reveal that DP-GNNs, which rely on graph convolutions, not only fail to meet the requirements for multigranular graph topology privacy but also necessitate the injection of DP noise that scales at least linearly with the maximum node degree. In contrast, our proposed Differentially Private Decoupled Graph Convolutions (DPDGCs) represent a more flexible and efficient alternative to graph convolutions that still provides the necessary guarantees of GDP. To validate our approach, we conducted extensive experiments on seven node classification benchmarking and illustrative synthetic datasets. The results demonstrate that DPDGCs significantly outperform existing DP-GNNs in terms of privacy-utility trade-offs.

Given a training set, a loss function, and a neural network architecture, it is often taken for granted that optimal network parameters exist, and a common practice is to apply available optimization algorithms to search for them. In this work, we show that the existence of an optimal solution is not always guaranteed, especially in the context of sparse ReLU neural networks. In particular, we first show that optimization problems involving deep networks with certain sparsity patterns do not always have optimal parameters, and that optimization algorithms may then diverge. Via a new topological relation between sparse ReLU neural networks and their linear counterparts, we derive --using existing tools from real algebraic geometry-- an algorithm to verify that a given sparsity pattern suffers from this issue. Then, the existence of a global optimum is proved for every concrete optimization problem involving a shallow sparse ReLU neural network of output dimension one. Overall, the analysis is based on the investigation of two topological properties of the space of functions implementable as sparse ReLU neural networks: a best approximation property, and a closedness property, both in the uniform norm. This is studied both for (finite) domains corresponding to practical training on finite training sets, and for more general domains such as the unit cube. This allows us to provide conditions for the guaranteed existence of an optimum given a sparsity pattern. The results apply not only to several sparsity patterns proposed in recent works on network pruning/sparsification, but also to classical dense neural networks, including architectures not covered by existing results.

This paper presents a collaborative implicit neural simultaneous localization and mapping (SLAM) system with RGB-D image sequences, which consists of complete front-end and back-end modules including odometry, loop detection, sub-map fusion, and global refinement. In order to enable all these modules in a unified framework, we propose a novel neural point based 3D scene representation in which each point maintains a learnable neural feature for scene encoding and is associated with a certain keyframe. Moreover, a distributed-to-centralized learning strategy is proposed for the collaborative implicit SLAM to improve consistency and cooperation. A novel global optimization framework is also proposed to improve the system accuracy like traditional bundle adjustment. Experiments on various datasets demonstrate the superiority of the proposed method in both camera tracking and mapping.

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate very complex solution functions. The number of training points (collocation points) required on these challenging PDEs grows substantially, and it is severely limited due to the expensive computational costs and heavy memory overhead. To overcome this limit, we propose a network architecture and training algorithm for PINNs. The proposed method, separable PINN (SPINN), operates on a per-axis basis to decrease the number of network propagations in multi-dimensional PDEs instead of point-wise processing in conventional PINNs. We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points ($>10^7$) on a single commodity GPU. The experimental results show significantly reduced computational costs ($62\times$ in wall-clock time, $1,394\times$ in FLOPs given the same number of collocation points) in multi-dimensional PDEs while achieving better accuracy. Furthermore, we present that SPINN can solve a chaotic (2+1)-d Navier-Stokes equation much faster than the best-performing prior method (9 minutes vs. 10 hours in a single GPU), maintaining accuracy. Finally, we showcase that SPINN can accurately obtain the solution of a highly nonlinear and multi-dimensional PDE, a (3+1)-d Navier-Stokes equation. For visualized results and code, please see https://jwcho5576.github.io/spinn.github.io/.

We study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is $O(1)$ in the number of nodes, in the fixed-dimensional asymptotic regime, i.e., the dimension of the feature data is fixed while the number of nodes is large. Such graphs are typically known to be locally tree-like. We introduce a notion of Bayes optimality for node classification tasks, called asymptotic local Bayes optimality, and compute the optimal classifier according to this criterion for a fairly general statistical data model with arbitrary distributions of the node features and edge connectivity. The optimal classifier is implementable using a message-passing graph neural network architecture. We then compute the generalization error of this classifier and compare its performance against existing learning methods theoretically on a well-studied statistical model with naturally identifiable signal-to-noise ratios (SNRs) in the data. We find that the optimal message-passing architecture interpolates between a standard MLP in the regime of low graph signal and a typical convolution in the regime of high graph signal. Furthermore, we prove a corresponding non-asymptotic result.

In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples ($\textit{sampler-only}$ network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits $\textit{reservoir-sampler networks}$ (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based Bayesian brain models.

ReLU networks have remained the default choice for models in the area of image prediction despite their well-established spectral bias towards learning low frequencies faster, and consequently their difficulty of reproducing high frequency visual details. As an alternative, sin networks showed promising results in learning implicit representations of visual data. However training these networks in practically relevant settings proved to be difficult, requiring careful initialization, dealing with issues due to inconsistent gradients, and a degeneracy in local minima. In this work, we instead propose replacing a baseline network’s existing activations with a novel ensemble function with trainable parameters. The proposed MetaSin activation can be trained reliably without requiring intricate initialization schemes, and results in consistently lower test loss compared to alternatives. We demonstrate our method in the areas of Monte-Carlo denoising and image resampling where we set new state-of-the-art through a knowledge distillation based training procedure. We present ablations on hyper-parameter settings, comparisons with alternative activation function formulations, and discuss the use of our method in other domains, such as image classification.

Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn over manifold-valued data encountered in the natural sciences. These networks are often inspired by and directly generalize standard Euclidean neural networks. However, extending Euclidean networks is difficult and has only been done for a select few manifolds. In this work, we examine the residual neural network (ResNet) and show how to extend this construction to general Riemannian manifolds in a geometrically principled manner. Originally introduced to help solve the vanishing gradient problem, ResNets have become ubiquitous in machine learning due to their beneficial learning properties, excellent empirical results, and easy-to-incorporate nature when building varied neural networks. We find that our Riemannian ResNets mirror these desirable properties: when compared to existing manifold neural networks designed to learn over hyperbolic space and the manifold of symmetric positive definite matrices, we outperform both kinds of networks in terms of relevant testing metrics and training dynamics.

Motion planning, which aims to find a high-quality collision-free path in the configuration space, is a fundamental task in robotic systems. Recently, learning-based motion planners, especially the graph neural network-powered, have shown promising planning performance. However, though the state-of-the-art GNN planner can efficiently extract and learn graph information, its inherent mechanism is not well suited for graph search process, hindering its further performance improvement. To address this challenge and fully unleash the potential of GNN in motion planning, this paper proposes GraphMP, a neural motion planner for both low and high-dimensional planning tasks. With the customized model architecture and training mechanism design, GraphMP can simultaneously perform efficient graph pattern extraction and graph search processing, leading to strong planning performance. Experiments on a variety of environments, ranging from 2D Maze to 14D dual KUKA robotic arm, show that our proposed GraphMP achieves significant improvement on path quality and planning speed over the state-of-the-art learning-based and classical planners; while preserving the competitive success rate.

In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap") can capture accelerated aging due to adverse health conditions and therefore, can reflect increased vulnerability towards neurological disease or cognitive impairments. However, widespread adoption of brain age for clinical decision support has been hindered due to lack of transparency and methodological justifications in most existing brain age prediction algorithms. In this paper, we leverage coVariance neural networks (VNN) to propose an explanation-driven and anatomically interpretable framework for brain age prediction using cortical thickness features. Specifically, our brain age prediction framework extends beyond the coarse metric of brain age gap in Alzheimer’s disease (AD) and we make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD by identifying contributing brain regions, (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific eigenvectors of the anatomical covariance matrix. Together, these observations facilitate an explainable and anatomically interpretable perspective to the task of brain age prediction.

Nowadays integrated circuits (ICs) are underpinning all major information technology innovations including the current trends of artificial intelligence (AI). Modern IC designs often involve analyses of complex phenomena (such as timing, noise, and power etc.) for tens of billions of electronic components, like resistance (R), capacitance (C), transistors and gates, interconnected in various complex structures. Those analyses often need to strike a balance between accuracy and speed as those analyses need to be carried out many times throughout the entire IC design cycles. With the advancement of AI, researchers also start to explore news ways in leveraging AI to improve those analyses. This paper focuses on one of the most important analyses, timing analysis for interconnects. Since IC interconnects can be represented as an RC-tree, a specialized graph as tree, we design a novel tree-based graph neural network, SyncTREE, to speed up the timing analysis by incorporating both the structural and physical properties of electronic circuits. Our major innovations include (1) a two-pass message-passing (bottom-up and top-down) for graph embedding, (2) a tree contrastive loss to guide learning, and (3) a closed formular-based approach to conduct fast timing. Our experiments show that, compared to conventional GNN models, SyncTREE achieves the best timing prediction in terms of both delays and slews, all in reference to the industry golden numerical analyses results on real IC design data.

Symmetries have been leveraged to improve the generalization of neural networks through different mechanisms from data augmentation to equivariant architectures. However, despite their potential, their integration into neural solvers for partial differential equations (PDEs) remains largely unexplored. We explore the integration of PDE symmetries, known as Lie point symmetries, in a major family of neural solvers known as physics-informed neural networks (PINNs). We propose a loss function that informs the network about Lie point symmetries in the same way that PINN models try to enforce the underlying PDE through a loss function. Intuitively, our symmetry loss ensures that the infinitesimal generators of the Lie group conserve the PDE solutions.. Effectively, this means that once the network learns a solution, it also learns the neighbouring solutions generated by Lie point symmetries. Empirical evaluations indicate that the inductive bias introduced by the Lie point symmetries of the PDEs greatly boosts the sample efficiency of PINNs.

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed by minimizing a divergence measure between the posterior conditioning on the pseudocoreset and the posterior conditioning on the full dataset. However, evaluating the divergence can be challenging, particularly for the models like deep neural networks having high-dimensional parameters. In this paper, we propose a novel Bayesian pseudocoreset construction method that operates on a function space. Unlike previous methods, which construct and match the coreset and full data posteriors in the space of model parameters (weights), our method constructs variational approximations to the coreset posterior on a function space and matches it to the full data posterior in the function space. By working directly on the function space, our method could bypass several challenges that may arise when working on a weight space, including limited scalability and multi-modality issue. Through various experiments, we demonstrate that the Bayesian pseudocoresets constructed from our method enjoys enhanced uncertainty quantification and better robustness across various model architectures.

Bayesian neural networks often approximate the weight-posterior with a Gaussian distribution. However, practical posteriors are often, even locally, highly non-Gaussian, and empirical performance deteriorates. We propose a simple parametric approximate posterior that adapts to the shape of the true posterior through a Riemannian metric that is determined by the log-posterior gradient. We develop a Riemannian Laplace approximation where samples naturally fall into weight-regions with low negative log-posterior. We show that these samples can be drawn by solving a system of ordinary differential equations, which can be done efficiently by leveraging the structure of the Riemannian metric and automatic differentiation. Empirically, we demonstrate that our approach consistently improves over the conventional Laplace approximation across tasks. We further show that, unlike the conventional Laplace approximation, our method is not overly sensitive to the choice of prior, which alleviates a practical pitfall of current approaches.

Real-world adversarial attacks on machine learning models often feature an asymmetric structure wherein adversaries only attempt to induce false negatives (e.g., classify a spam email as not spam). We formalize the asymmetric robustness certification problem and correspondingly present the feature-convex neural network architecture, which composes an input-convex neural network (ICNN) with a Lipschitz continuous feature map in order to achieve asymmetric adversarial robustness. We consider the aforementioned binary setting with one "sensitive" class, and for this class we prove deterministic, closed-form, and easily-computable certified robust radii for arbitrary $\ell_p$-norms. We theoretically justify the use of these models by characterizing their decision region geometry, extending the universal approximation theorem for ICNN regression to the classification setting, and proving a lower bound on the probability that such models perfectly fit even unstructured uniformly distributed data in sufficiently high dimensions. Experiments on Malimg malware classification and subsets of the MNIST, Fashion-MNIST, and CIFAR-10 datasets show that feature-convex classifiers attain substantial certified $\ell_1$, $\ell_2$, and $\ell_{\infty}$-radii while being far more computationally efficient than competitive baselines.

Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish {the forecasting}. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods. Code is available at this repository: https://github.com/aikunyi/FourierGNN.