NeurIPS 2023 论文列表

We consider the algorithmic problem of finding the optimal weights and biases for a two-layer fully connected neural network to fit a given set of data points, also known as empirical risk minimization. We show that the problem is $\exists\mathbb{R}$-complete. This complexity class can be defined as the set of algorithmic problems that are polynomial-time equivalent to finding real roots of a multivariate polynomial with integer coefficients. Furthermore, we show that arbitrary algebraic numbers are required as weights to be able to train some instances to optimality, even if all data points are rational. Our result already applies to fully connected instances with two inputs, two outputs, and one hidden layer of ReLU neurons. Thereby, we strengthen a result by Abrahamsen, Kleist and Miltzow [NeurIPS 2021]. A consequence of this is that a combinatorial search algorithm like the one by Arora, Basu, Mianjy and Mukherjee [ICLR 2018] is impossible for networks with more than one output dimension, unless $\text{NP} = \exists\mathbb{R}$.

Feedforward generalizable models for implicit shape reconstruction from unoriented point cloud present multiple advantages, including high performance and inference speed. However, they still suffer from generalization issues, ranging from underfitting the input point cloud, to misrepresenting samples outside of the training data distribution, or with toplogies unseen at training. We propose here an efficient mechanism to remedy some of these limitations at test time. We combine the inter-shape data prior of the network with an intra-shape regularization prior of a Nyström Kernel Ridge Regression, that we further adapt by fitting its hyperprameters to the current shape. The resulting shape function defined in a shape specific Reproducing Kernel Hilbert Space benefits from desirable stability and efficiency properties and grants a shape adaptive expressiveness-robustness trade-off. We demonstrate the improvement obtained through our method with respect to baselines and the state-of-the-art using synthetic and real data.

Despite its success in the image domain, adversarial training did not (yet) stand out as an effective defense for Graph Neural Networks (GNNs) against graph structure perturbations. In the pursuit of fixing adversarial training (1) we show and overcome fundamental theoretical as well as practical limitations of the adopted graph learning setting in prior work; (2) we reveal that flexible GNNs based on learnable graph diffusion are able to adjust to adversarial perturbations, while the learned message passing scheme is naturally interpretable; (3) we introduce the first attack for structure perturbations that, while targeting multiple nodes at once, is capable of handling global (graph-level) as well as local (node-level) constraints. Including these contributions, we demonstrate that adversarial training is a state-of-the-art defense against adversarial structure perturbations.

The widespread deployment of Graph Neural Networks (GNNs) sparks significant interest in their explainability, which plays a vital role in model auditing and ensuring trustworthy graph learning. The objective of GNN explainability is to discern the underlying graph structures that have the most significant impact on model predictions. Ensuring that explanations generated are reliable necessitates consideration of the in-distribution property, particularly due to the vulnerability of GNNs to out-of-distribution data. Unfortunately, prevailing explainability methods tend to constrain the generated explanations to the structure of the original graph, thereby downplaying the significance of the in-distribution property and resulting in explanations that lack reliability. To address these challenges, we propose D4Explainer, a novel approach that provides in-distribution GNN explanations for both counterfactual and model-level explanation scenarios. The proposed D4Explainer incorporates generative graph distribution learning into the optimization objective, which accomplishes two goals: 1) generate a collection of diverse counterfactual graphs that conform to the in-distribution property for a given instance, and 2) identify the most discriminative graph patterns that contribute to a specific class prediction, thus serving as model-level explanations. It is worth mentioning that D4Explainer is the first unified framework that combines both counterfactual and model-level explanations. Empirical evaluations conducted on synthetic and real-world datasets provide compelling evidence of the state-of-the-art performance achieved by D4Explainer in terms of explanation accuracy, faithfulness, diversity, and robustness.

Advances in optical and electrophysiological recording technologies have made it possible to record the dynamics of thousands of neurons, opening up new possibilities for interpreting and controlling large neural populations in behaving animals. A promising way to extract computational principles from these large datasets is to train data-constrained recurrent neural networks (dRNNs). Performing this training in real-time could open doors for research techniques and medical applications to model and control interventions at single-cell resolution and drive desired forms of animal behavior. However, existing training algorithms for dRNNs are inefficient and have limited scalability, making it a challenge to analyze large neural recordings even in offline scenarios. To address these issues, we introduce a training method termed Convex Optimization of Recurrent Neural Networks (CORNN). In studies of simulated recordings, CORNN attained training speeds $\sim$100-fold faster than traditional optimization approaches while maintaining or enhancing modeling accuracy. We further validated CORNN on simulations with thousands of cells that performed simple computations such as those of a 3-bit flip-flop or the execution of a timed response. Finally, we showed that CORNN can robustly reproduce network dynamics and underlying attractor structures despite mismatches between generator and inference models, severe subsampling of observed neurons, or mismatches in neural time-scales. Overall, by training dRNNs with millions of parameters in subminute processing times on a standard computer, CORNN constitutes a first step towards real-time network reproduction constrained on large-scale neural recordings and a powerful computational tool for advancing the understanding of neural computation.

The McKean-Vlasov equation (MVE) describes the collective behavior of particles subject to drift, diffusion, and mean-field interaction. In physical systems, the interaction term can be singular, i.e. it diverges when two particles collide. Notable examples of such interactions include the Coulomb interaction, fundamental in plasma physics, and the Biot-Savart interaction, present in the vorticity formulation of the 2D Navier-Stokes equation (NSE) in fluid dynamics. Solving MVEs that involve singular interaction kernels presents a significant challenge, especially when aiming to provide rigorous theoretical guarantees. In this work, we propose a novel approach based on the concept of entropy dissipation in the underlying system. We derive a potential function that effectively controls the KL divergence between a hypothesis solution and the ground truth. Building upon this theoretical foundation, we introduce the Entropy-dissipation Informed Neural Network (EINN) framework for solving MVEs. In EINN, we utilize neural networks (NN) to approximate the underlying velocity field and minimize the proposed potential function. By leveraging the expressive power of NNs, our approach offers a promising avenue for tackling the complexities associated with singular interactions. To assess the empirical performance of our method, we compare EINN with SOTA NN-based MVE solvers. The results demonstrate the effectiveness of our approach in solving MVEs across various example problems.

Graph Neural Networks (GNNs) have achieved remarkable success in various applications, but their performance can be sensitive to specific data properties of the graph datasets they operate on. Current literature on understanding the limitations of GNNs has primarily employed a \emph{model-driven} approach that leverage heuristics and domain knowledge from network science or graph theory to model the GNN behaviors, which is time-consuming and highly subjective. In this work, we propose a \emph{metadata-driven} approach to analyze the sensitivity of GNNs to graph data properties, motivated by the increasing availability of graph learning benchmarks. We perform a multivariate sparse regression analysis on the metadata derived from benchmarking GNN performance across diverse datasets, yielding a set of salient data properties. To validate the effectiveness of our data-driven approach, we focus on one identified data property, the degree distribution, and investigate how this property influences GNN performance through theoretical analysis and controlled experiments. Our theoretical findings reveal that datasets with more balanced degree distribution exhibit better linear separability of node representations, thus leading to better GNN performance. We also conduct controlled experiments using synthetic datasets with varying degree distributions, and the results align well with our theoretical findings. Collectively, both the theoretical analysis and controlled experiments verify that the proposed metadata-driven approach is effective in identifying critical data properties for GNNs.

This paper studies the behaviour of two-layer fully connected networks with linear activations trained with gradient flow on the square loss. We show how the optimization process carries an implicit bias on the parameters that depends on the scale of its initialization. The main result of the paper is a variational characterization of the loss minimizers retrieved by the gradient flow for a specific initialization shape. This characterization reveals that, in the small scale initialization regime, the linear neural network's hidden layer is biased toward having a low-rank structure. To complement our results, we showcase a hidden mirror flow that tracks the dynamics of the singular values of the weights matrices and describe their time evolution. We support our findings with numerical experiments illustrating the phenomena.

Given the rich visual information available in each glance, humans can internally direct their visual attention to enhance goal-relevant information---a capacity often absent in standard vision models. Here we introduce cognitively and biologically-inspired long-range modulatory pathways to enable `cognitive steering’ in vision models. First, we show that models equipped with these feedback pathways naturally show improved image recognition, adversarial robustness, and increased brain alignment, relative to baseline models. Further, these feedback projections from the final layer of the vision backbone provide a meaningful steering interface, where goals can be specified as vectors in the output space. We show that there are effective ways to steer the model that dramatically improve recognition of categories in composite images of multiple categories, succeeding where baseline feed-forward models without flexible steering fail. And, our multiplicative modulatory motif prevents rampant hallucination of the top-down goal category, dissociating what the model is looking for, from what it is looking at. Thus, these long-range modulatory pathways enable new behavioral capacities for goal-directed visual encoding, offering a flexible communication interface between cognitive and visual systems.

The core components of many modern neural network architectures, such as transformers, convolutional, or graph neural networks, can be expressed as linear layers with *weight-sharing*. Kronecker-Factored Approximate Curvature (K-FAC), a second-order optimisation method, has shown promise to speed up neural network training and thereby reduce computational costs. However, there is currently no framework to apply it to generic architectures, specifically ones with linear weight-sharing layers. In this work, we identify two different settings of linear weight-sharing layers which motivate two flavours of K-FAC -- *expand* and *reduce*. We show that they are exact for deep linear networks with weight-sharing in their respective setting. Notably, K-FAC-reduce is generally faster than K-FAC-expand, which we leverage to speed up automatic hyperparameter selection via optimising the marginal likelihood for a Wide ResNet. Finally, we observe little difference between these two K-FAC variations when using them to train both a graph neural network and a vision transformer. However, both variations are able to reach a fixed validation metric target in $50$-$75$\% of the number of steps of a first-order reference run, which translates into a comparable improvement in wall-clock time. This highlights the potential of applying K-FAC to modern neural network architectures.

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.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve SE(3)-equivariance by design. From the graph spectrum view, our method can be interpreted as convolution on graphons (dense graphs with infinitely many nodes), which we term InfGCN. By leveraging both the continuous graphon structure and the discrete graph structure of the input data, our model can effectively capture the geometric information while preserving equivariance. Through extensive experiments on large-scale electron density datasets, we observed that our model significantly outperformed the current state-of-the-art architectures. Multiple ablation studies were also carried out to demonstrate the effectiveness of the proposed architecture.

We describe a new setting for learning a deep graph generative model (GGM) from aggregate graph statistics, rather than from the graph adjacency matrix. Matching the statistics of observed training graphs is the main approach for learning traditional GGMs (e.g, BTER, Chung-Lu, and Erdos-Renyi models). Privacy researchers have proposed learning from graph statistics as a way to protect privacy. We develop an architecture for training a deep GGM to match statistics while preserving local differential privacy guarantees. Empirical evaluation on 8 datasets indicates that our deep GGM model generates more realistic graphs than the traditional GGMs when both are learned from graph statistics only. We also benchmark our deep GGM trained on statistics only, against state-of-the-art deep GGM models that are trained on the entire adjacency matrix. The results show that graph statistics are often sufficient to build a competitive deep GGM that generates realistic graphs while protecting local privacy.

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models. For example, group equivariant neural networks have demonstrated impressive performance across various domains and applications such as protein and drug design. A prevalent intuition about such models is that the integration of relevant symmetry results in enhanced generalization. Moreover, it is posited that when the data and/or the model exhibits only approximate or partial symmetry, the optimal or best-performing model is one where the model symmetry aligns with the data symmetry. In this paper, we conduct a formal unified investigation of these intuitions. To begin, we present quantitative bounds that demonstrate how models capturing task-specific symmetries lead to improved generalization. Utilizing this quantification, we examine the more general question of dealing with approximate/partial symmetries. We establish, for a given symmetry group, a quantitative comparison between the approximate equivariance of the model and that of the data distribution, precisely connecting model equivariance error and data equivariance error. Our result delineates the conditions under which the model equivariance error is optimal, thereby yielding the best-performing model for the given task and data.

As more deep learning models are being applied in real-world applications, there is a growing need for modeling and learning the representations of neural networks themselves. An effective representation can be used to predict target attributes of networks without the need for actual training and deployment procedures, facilitating efficient network design and deployment. Recently, inspired by the success of Transformer, some Transformer-based representation learning frameworks have been proposed and achieved promising performance in handling cell-structured models. However, graph neural network (GNN) based approaches still dominate the field of learning representation for the entire network. In this paper, we revisit the Transformer and compare it with GNN to analyze their different architectural characteristics. We then propose a modified Transformer-based universal neural network representation learning model NAR-Former V2. It can learn efficient representations from both cell-structured networks and entire networks. Specifically, we first take the network as a graph and design a straightforward tokenizer to encode the network into a sequence. Then, we incorporate the inductive representation learning capability of GNN into Transformer, enabling Transformer to generalize better when encountering unseen architecture. Additionally, we introduce a series of simple yet effective modifications to enhance the ability of the Transformer in learning representation from graph structures. In encoding entire networks and then predicting the latency, our proposed method surpasses the GNN-based method NNLP by a significant margin on the NNLQP dataset. Furthermore, regarding accuracy prediction on the cell-structured NASBench101 and NASBench201 datasets, our method achieves highly comparable performance to other state-of-the-art methods. The code is available at https://github.com/yuny220/NAR-Former-V2.

Crystal Structure Prediction (CSP) is crucial in various scientific disciplines. While CSP can be addressed by employing currently-prevailing generative models (**e.g.** diffusion models), this task encounters unique challenges owing to the symmetric geometry of crystal structures---the invariance of translation, rotation, and periodicity. To incorporate the above symmetries, this paper proposes DiffCSP, a novel diffusion model to learn the structure distribution from stable crystals. To be specific, DiffCSP jointly generates the lattice and atom coordinates for each crystal by employing a periodic-E(3)-equivariant denoising model, to better model the crystal geometry. Notably, different from related equivariant generative approaches, DiffCSP leverages fractional coordinates other than Cartesian coordinates to represent crystals, remarkably promoting the diffusion and the generation process of atom positions. Extensive experiments verify that our DiffCSP remarkably outperforms existing CSP methods, with a much lower computation cost in contrast to DFT-based methods. Moreover, the superiority of DiffCSP is still observed when it is extended for ab initio crystal generation.

Recent years have witnessed significant progress in understanding the relationship between the connectivity of a deep network's architecture as a graph, and the network's performance. A few prior arts connected deep architectures to expander graphs or Ramanujan graphs, and particularly,[7] demonstrated the use of such graph connectivity measures with ranking and relative performance of various obtained sparse sub-networks (i.e. models with prune masks) without the need for training. However, no prior work explicitly explores the role of parameters in the graph's connectivity, making the graph-based understanding of prune masks and the magnitude/gradient-based pruning practice isolated from one another. This paper strives to fill in this gap, by analyzing the Weighted Spectral Gap of Ramanujan structures in sparse neural networks and investigates its correlation with final performance. We specifically examine the evolution of sparse structures under a popular dynamic sparse-to-sparse network training scheme, and intriguingly find that the generated random topologies inherently maximize Ramanujan graphs. We also identify a strong correlation between masks, performance, and the weighted spectral gap. Leveraging this observation, we propose to construct a new "full-spectrum coordinate'' aiming to comprehensively characterize a sparse neural network's promise. Concretely, it consists of the classical Ramanujan's gap (structure), our proposed weighted spectral gap (parameters), and the constituent nested regular graphs within. In this new coordinate system, a sparse subnetwork's L2-distance from its original initialization is found to have nearly linear correlated with its performance. Eventually, we apply this unified perspective to develop a new actionable pruning method, by sampling sparse masks to maximize the L2-coordinate distance. Our method can be augmented with the "pruning at initialization" (PaI) method, and significantly outperforms existing PaI methods. With only a few iterations of training (e.g 500 iterations), we can get LTH-comparable performance as that yielded via "pruning after training", significantly saving pre-training costs. Codes can be found at: https://github.com/VITA-Group/FullSpectrum-PAI.

Graph neural networks (GNNs) are the de facto standard deep learning architectures for machine learning on graphs. This has led to a large body of work analyzing the capabilities and limitations of these models, particularly pertaining to their representation and extrapolation capacity. We offer a novel theoretical perspective on the representation and extrapolation capacity of GNNs, by answering the question: how do GNNs behave as the number of graph nodes become very large? Under mild assumptions, we show that when we draw graphs of increasing size from the Erdős–Rényi model, the probability that such graphs are mapped to a particular output by a class of GNN classifiers tends to either zero or one. This class includes the popular graph convolutional network architecture. The result establishes `zero-one laws' for these GNNs, and analogously to other convergence laws, entails theoretical limitations on their capacity. We empirically verify our results, observing that the theoretical asymptotic limits are evident already on relatively small graphs.