NeurIPS 2023 Papers

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.

We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$\beta$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.

Knowledge tracing (KT) aims to trace students' knowledge states by predicting whether students answer correctly on exercises. Despite the excellent performance of existing Transformer-based KT approaches, they are criticized for the manually selected input features for fusion and the defect of single global context modelling to directly capture students' forgetting behavior in KT, when the related records are distant from the current record in terms of time. To address the issues, this paper first considers adding convolution operations to the Transformer to enhance its local context modelling ability used for students' forgetting behavior, then proposes an evolutionary neural architecture search approach to automate the input feature selection and automatically determine where to apply which operation for achieving the balancing of the local/global context modelling. In the search space, the original global path containing the attention module in Transformer is replaced with the sum of a global path and a local path that could contain different convolutions, and the selection of input features is also considered. To search the best architecture, we employ an effective evolutionary algorithm to explore the search space and also suggest a search space reduction strategy to accelerate the convergence of the algorithm. Experimental results on the two largest and most challenging education datasets demonstrate the effectiveness of the architecture found by the proposed approach.

The human visual system uses two parallel pathways for spatial processing and object recognition. In contrast, computer vision systems tend to use a single feedforward pathway, rendering them less robust, adaptive, or efficient than human vision. To bridge this gap, we developed a dual-stream vision model inspired by the human eyes and brain. At the input level, the model samples two complementary visual patterns to mimic how the human eyes use magnocellular and parvocellular retinal ganglion cells to separate retinal inputs to the brain. At the backend, the model processes the separate input patterns through two branches of convolutional neural networks (CNN) to mimic how the human brain uses the dorsal and ventral cortical pathways for parallel visual processing. The first branch (WhereCNN) samples a global view to learn spatial attention and control eye movements. The second branch (WhatCNN) samples a local view to represent the object around the fixation. Over time, the two branches interact recurrently to build a scene representation from moving fixations. We compared this model with the human brains processing the same movie and evaluated their functional alignment by linear transformation. The WhereCNN and WhatCNN branches were found to differentially match the dorsal and ventral pathways of the visual cortex, respectively, primarily due to their different learning objectives, rather than their distinctions in retinal sampling or sensitivity to attention-driven eye movements. These model-based results lead us to speculate that the distinct responses and representations of the ventral and dorsal streams are more influenced by their distinct goals in visual attention and object recognition than by their specific bias or selectivity in retinal inputs. This dual-stream model takes a further step in brain-inspired computer vision, enabling parallel neural networks to actively explore and understand the visual surroundings.

Recent advances in neural image compression (NIC) have produced models that are starting to outperform classic codecs. While this has led to growing excitement about using NIC in real-world applications, the successful adoption of any machine learning system in the wild requires it to generalize (and be robust) to unseen distribution shifts at deployment. Unfortunately, current research lacks comprehensive datasets and informative tools to evaluate and understand NIC performance in real-world settings. To bridge this crucial gap, first, this paper presents a comprehensive benchmark suite to evaluate the out-of-distribution (OOD) performance of image compression methods. Specifically, we provide CLIC-C and Kodak-C by introducing 15 corruptions to the popular CLIC and Kodak benchmarks. Next, we propose spectrally-inspired inspection tools to gain deeper insight into errors introduced by image compression methods as well as their OOD performance. We then carry out a detailed performance comparison of several classic codecs and NIC variants, revealing intriguing findings that challenge our current understanding of the strengths and limitations of NIC. Finally, we corroborate our empirical findings with theoretical analysis, providing an in-depth view of the OOD performance of NIC and its dependence on the spectral properties of the data. Our benchmarks, spectral inspection tools, and findings provide a crucial bridge to the real-world adoption of NIC. We hope that our work will propel future efforts in designing robust and generalizable NIC methods. Code and data will be made available at https://github.com/klieberman/ood_nic.

Remarkable progress has been made in 3D reconstruction from single-view RGB-D inputs. MCC is the current state-of-the-art method in this field, which achieves unprecedented success by combining vision Transformers with large-scale training. However, we identified two key limitations of MCC: 1) The Transformer decoder is inefficient in handling large number of query points; 2) The 3D representation struggles to recover high-fidelity details. In this paper, we propose a new approach called NU-MCC that addresses these limitations. NU-MCC includes two key innovations: a Neighborhood decoder and a Repulsive Unsigned Distance Function (Repulsive UDF). First, our Neighborhood decoder introduces center points as an efficient proxy of input visual features, allowing each query point to only attend to a small neighborhood. This design not only results in much faster inference speed but also enables the exploitation of finer-scale visual features for improved recovery of 3D textures. Second, our Repulsive UDF is a novel alternative to the occupancy field used in MCC, significantly improving the quality of 3D object reconstruction. Compared to standard UDFs that suffer from holes in results, our proposed Repulsive UDF can achieve more complete surface reconstruction. Experimental results demonstrate that NU-MCC is able to learn a strong 3D representation, significantly advancing the state of the art in single-view 3D reconstruction. Particularly, it outperforms MCC by 9.7% in terms of the F1-score on the CO3D-v2 dataset with more than 5x faster running speed.

Recently, Spiking Neural Networks (SNNs), enjoying extreme energy efficiency, have drawn much research attention on 2D visual recognition and shown gradually increasing application potential. However, it still remains underexplored whether SNNs can be generalized to 3D recognition. To this end, we present Spiking PointNet in the paper, the first spiking neural model for efficient deep learning on point clouds. We discover that the two huge obstacles limiting the application of SNNs in point clouds are: the intrinsic optimization obstacle of SNNs that impedes the training of a big spiking model with large time steps, and the expensive memory and computation cost of PointNet that makes training a big spiking point model unrealistic. To solve the problems simultaneously, we present a trained-less but learning-more paradigm for Spiking PointNet with theoretical justifications and in-depth experimental analysis. In specific, our Spiking PointNet is trained with only a single time step but can obtain better performance with multiple time steps inference, compared to the one trained directly with multiple time steps. We conduct various experiments on ModelNet10, ModelNet40 to demonstrate the effectiveness of Sipiking PointNet. Notably, our Spiking PointNet even can outperform its ANN counterpart, which is rare in the SNN field thus providing a potential research direction for the following work. Moreover, Spiking PointNet shows impressive speedup and storage saving in the training phase. Our code is open-sourced at https://github.com/DayongRen/Spiking-PointNet.

Learning continuous-time point processes is essential to many discrete event forecasting tasks. However, integration poses a major challenge, particularly for spatiotemporal point processes (STPPs), as it involves calculating the likelihood through triple integrals over space and time. Existing methods for integrating STPP either assume a parametric form of the intensity function, which lacks flexibility; or approximating the intensity with Monte Carlo sampling, which introduces numerical errors. Recent work by Omi et al. proposes a dual network approach for efficient integration of flexible intensity function. However, their method only focuses on the 1D temporal point process. In this paper, we introduce a novel paradigm: `Auto-STPP` (Automatic Integration for Spatiotemporal Neural Point Processes) that extends the dual network approach to 3D STPP. While previous work provides a foundation, its direct extension overly restricts the intensity function and leads to computational challenges. In response, we introduce a decomposable parametrization for the integral network using ProdNet. This approach, leveraging the product of simplified univariate graphs, effectively sidesteps the computational complexities inherent in multivariate computational graphs. We prove the consistency of `Auto-STPP` and validate it on synthetic data and benchmark real-world datasets. `Auto-STPP` shows a significant advantage in recovering complex intensity functions from irregular spatiotemporal events, particularly when the intensity is sharply localized. Our code is open-source at https://github.com/Rose-STL-Lab/AutoSTPP.

We propose a foundation model named Brant for modeling intracranial recordings, which learns powerful representations of intracranial neural signals by pre-training, providing a large-scale, off-the-shelf model for medicine. Brant is the largest model in the field of brain signals and is pre-trained on a large corpus of intracranial data collected by us. The design of Brant is to capture long-term temporal dependency and spatial correlation from neural signals, combining the information in both time and frequency domains. As a foundation model, Brant achieves SOTA performance on various downstream tasks (i.e. neural signal forecasting, frequency-phase forecasting, imputation and seizure detection), showing the generalization ability to a broad range of tasks. The low-resource label analysis and representation visualization further illustrate the effectiveness of our pre-training strategy. In addition, we explore the effect of model size to show that a larger model with a higher capacity can lead to performance improvements on our dataset. The source code and pre-trained weights are available at: https://zju-brainnet.github.io/Brant.github.io/.

Within a single sniff, the mammalian olfactory system can decode the identity and concentration of odorants wafted on turbulent plumes of air. Yet, it must do so given access only to the noisy, dimensionally-reduced representation of the odor world provided by olfactory receptor neurons. As a result, the olfactory system must solve a compressed sensing problem, relying on the fact that only a handful of the millions of possible odorants are present in a given scene. Inspired by this principle, past works have proposed normative compressed sensing models for olfactory decoding. However, these models have not captured the unique anatomy and physiology of the olfactory bulb, nor have they shown that sensing can be achieved within the 100-millisecond timescale of a single sniff. Here, we propose a rate-based Poisson compressed sensing circuit model for the olfactory bulb. This model maps onto the neuron classes of the olfactory bulb, and recapitulates salient features of their connectivity and physiology. For circuit sizes comparable to the human olfactory bulb, we show that this model can accurately detect tens of odors within the timescale of a single sniff. We also show that this model can perform Bayesian posterior sampling for accurate uncertainty estimation. Fast inference is possible only if the geometry of the neural code is chosen to match receptor properties, yielding a distributed neural code that is not axis-aligned to individual odor identities. Our results illustrate how normative modeling can help us map function onto specific neural circuits to generate new hypotheses.

Tabular data is one of the most commonly used types of data in machine learning. Despite recent advances in neural nets (NNs) for tabular data, there is still an active discussion on whether or not NNs generally outperform gradient-boosted decision trees (GBDTs) on tabular data, with several recent works arguing either that GBDTs consistently outperform NNs on tabular data, or vice versa. In this work, we take a step back and question the importance of this debate. To this end, we conduct the largest tabular data analysis to date, comparing 19 algorithms across 176 datasets, and we find that the 'NN vs. GBDT' debate is overemphasized: for a surprisingly high number of datasets, either the performance difference between GBDTs and NNs is negligible, or light hyperparameter tuning on a GBDT is more important than choosing between NNs and GBDTs. Next, we analyze dozens of metafeatures to determine what \emph{properties} of a dataset make NNs or GBDTs better-suited to perform well. For example, we find that GBDTs are much better than NNs at handling skewed or heavy-tailed feature distributions and other forms of dataset irregularities. Our insights act as a guide for practitioners to determine which techniques may work best on their dataset. Finally, with the goal of accelerating tabular data research, we release the TabZilla Benchmark Suite: a collection of the 36 'hardest' of the datasets we study. Our benchmark suite, codebase, and all raw results are available at https://github.com/naszilla/tabzilla.

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.

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.

Despite the remarkable achievements of neural radiance fields (NeRF) in representing 3D scenes and generating novel view images, the aliasing issue, rendering 'jaggies' or 'blurry' images at varying camera distances, remains unresolved in most existing approaches. The recently proposed mip-NeRF has effectively addressed this challenge by introducing integrated positional encodings (IPE). However, it relies on MLP architecture to represent the radiance fields, missing out on the fast training speed offered by the latest grid-based methods. In this work, we present mip-Grid, a novel approach that integrates anti-aliasing techniques into grid-based representations for radiance fields, mitigating the aliasing artifacts while enjoying fast training time. Notably, the proposed method uses a single-scale shared grid representation and a single-sampling approach, which only introduces minimal additions to the model parameters and computational costs. To handle scale ambiguity, mip-Grid generates multiple grids by applying simple convolution operations over the shared grid and uses the scale-aware coordinate to retrieve the appropriate features from the generated multiple grids. To test the effectiveness, we incorporated the proposed approach into the two recent representative grid-based methods, TensoRF and K-Planes. The experimental results demonstrated that mip-Grid greatly improved the rendering performance of both methods and showed comparable performance to mip-NeRF on multi-scale datasets while achieving significantly faster training time.

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.

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.

The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient descent. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. However, all prior analyses assumed the infinite-particle or continuous-time limit, and cannot handle stochastic gradient updates. We provide a general framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and stochastic gradient. To demonstrate the wide applicability of our framework, we establish quantitative convergence rate guarantees to the regularized global optimal solution for $(i)$ a wide range of learning problems such as mean-field neural network and MMD minimization, and $(ii)$ different gradient estimators including SGD and SVRG. Despite the generality of our results, we achieve an improved convergence rate in both the SGD and SVRG settings when specialized to the standard Langevin dynamics.

We present a method that reconstructs and animates a 3D head avatar from a single-view portrait image. Existing methods either involve time-consuming optimization for a specific person with multiple images, or they struggle to synthesize intricate appearance details beyond the facial region. To address these limitations, we propose a framework that not only generalizes to unseen identities based on a single-view image without requiring person-specific optimization, but also captures characteristic details within and beyond the face area (e.g. hairstyle, accessories, etc.). At the core of our method are three branches that produce three tri-planes representing the coarse 3D geometry, detailed appearance of a source image, as well as the expression of a target image. By applying volumetric rendering to the combination of the three tri-planes followed by a super-resolution module, our method yields a high fidelity image of the desired identity, expression and pose. Once trained, our model enables efficient 3D head avatar reconstruction and animation via a single forward pass through a network. Experiments show that the proposed approach generalizes well to unseen validation datasets, surpassing SOTA baseline methods by a large margin on head avatar reconstruction and animation.

The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive power of GNNs. Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from the input graph, generating representations for each subgraph, and using them to augment the representation of the input graph. However, those methods require heavy preprocessing, and suffer from high time and memory costs. In this paper, we overcome the aforementioned limitations of subgraph GNNs by proposing a novel class of GNNs---$d$-Distance-Restricted FWL(2) GNNs, or $d$-DRFWL(2) GNNs, based on the well-known FWL(2) algorithm. As a heuristic method for graph isomorphism testing, FWL(2) colors all node pairs in a graph and performs message passing among those node pairs. In order to balance the expressive power and complexity, $d$-DRFWL(2) GNNs simplify FWL(2) by restricting the range of message passing to node pairs whose mutual distances are at most $d$. This way, $d$-DRFWL(2) GNNs exploit graph sparsity while avoiding the expensive subgraph extraction operations in subgraph GNNs, making both the time and space complexity lower. We theoretically investigate both the discriminative power and the cycle counting power of $d$-DRFWL(2) GNNs. Our most important finding is that $d$-DRFWL(2) GNNs have provably strong cycle counting power even with $d=2$: they can count all 3, 4, 5, 6-cycles. Since 6-cycles (e.g., benzene rings) are ubiquitous in organic molecules, being able to detect and count them is crucial for achieving robust and generalizable performance on molecular tasks. Experiments on both synthetic datasets and molecular datasets verify our theory. To the best of our knowledge, 2-DRFWL(2) GNN is the most efficient GNN model to date (both theoretically and empirically) that can count up to 6-cycles.