NeurIPS 2023 Papers

In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. Considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, while a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances in the design of pooling operators, there is not a principled criterion to compare them. In this work, we derive sufficient conditions for a pooling operator to fully preserve the expressive power of the MP layers before it. These conditions serve as a universal and theoretically-grounded criterion for choosing among existing pooling operators or designing new ones. Based on our theoretical findings, we analyze several existing pooling operators and identify those that fail to satisfy the expressiveness conditions. Finally, we introduce an experimental setup to verify empirically the expressive power of a GNN equipped with pooling layers, in terms of its capability to perform a graph isomorphism test.

We present a novel mechanism to improve the accuracy of the recently-introduced class of graph random features (GRFs). Our method induces negative correlations between the lengths of the algorithm's random walks by imposing antithetic termination: a procedure to sample more diverse random walks which may be of independent interest. It has a trivial drop-in implementation. We derive strong theoretical guarantees on the properties of these quasi-Monte Carlo GRFs (q-GRFs), proving that they yield lower-variance estimators of the $2$-regularised Laplacian kernel under mild conditions. Remarkably, our results hold for any graph topology. We demonstrate empirical accuracy improvements on a variety of tasks including a new practical application: time-efficient approximation of the graph diffusion process. To our knowledge, q-GRFs constitute the first rigorously studied quasi-Monte Carlo scheme for kernels defined on combinatorial objects, inviting new research on correlations between graph random walks.

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features.

Graph Neural Networks (GNNs) have emerged as the *de facto* standard for representation learning on graphs, owing to their ability to effectively integrate graph topology and node attributes. However, the inherent suboptimal nature of node connections, resulting from the complex and contingent formation process of graphs, presents significant challenges in modeling them effectively. To tackle this issue, Graph Structure Learning (GSL), a family of data-centric learning approaches, has garnered substantial attention in recent years. The core concept behind GSL is to jointly optimize the graph structure and the corresponding GNN models. Despite the proposal of numerous GSL methods, the progress in this field remains unclear due to inconsistent experimental protocols, including variations in datasets, data processing techniques, and splitting strategies. In this paper, we introduce OpenGSL, the first comprehensive benchmark for GSL, aimed at addressing this gap. OpenGSL enables a fair comparison among state-of-the-art GSL methods by evaluating them across various popular datasets using uniform data processing and splitting strategies. Through extensive experiments, we observe that existing GSL methods do not consistently outperform vanilla GNN counterparts. We also find that there is no significant correlation between the homophily of the learned structure and task performance, challenging the common belief. Moreover, we observe that the learned graph structure demonstrates a strong generalization ability across different GNN models, despite the high computational and space consumption. We hope that our open-sourced library will facilitate rapid and equitable evaluation and inspire further innovative research in this field. The code of the benchmark can be found in https://github.com/OpenGSL/OpenGSL.

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection to various stability notions such as BIBO stability, Lyapunov stability, structural stability, and conservative stability. We argue that Lyapunov stability, despite its common use, does not necessarily ensure adversarial robustness. Inspired by physics principles, we advocate for the use of conservative Hamiltonian neural flows to construct GNNs that are robust to adversarial attacks. The adversarial robustness of different neural flow GNNs is empirically compared on several benchmark datasets under a variety of adversarial attacks. Extensive numerical experiments demonstrate that GNNs leveraging conservative Hamiltonian flows with Lyapunov stability substantially improve robustness against adversarial perturbations. The implementation code of experiments is available at \url{https://github.com/zknus/NeurIPS-2023-HANG-Robustness}.

As graph neural networks (GNNs) struggle with large-scale graphs due to high computational demands, data distillation for graph data promises to alleviate this issue by distilling a large real graph into a smaller distilled graph while maintaining comparable prediction performance for GNNs trained on both graphs. However, we observe that GNNs trained on distilled graphs may exhibit more severe group fairness problems than those trained on real graphs. Motivated by this observation, we propose \textit{fair graph distillation} (\Algnameabbr), an approach for generating small distilled \textit{fair and informative} graphs based on the graph distillation method. The challenge lies in the deficiency of sensitive attributes for nodes in the distilled graph, making most debiasing methods (e.g., regularization and adversarial debiasing) intractable for distilled graphs. We develop a simple yet effective bias metric, called coherence, for distilled graphs. Based on the proposed coherence metric, we introduce a framework for fair graph distillation using a bi-level optimization algorithm. Extensive experiments demonstrate that the proposed algorithm can achieve better prediction performance-fairness trade-offs across various datasets and GNN architectures.

Graph Structure Learning (GSL) has recently garnered considerable attention due to its ability to optimize both the parameters of Graph Neural Networks (GNNs) and the computation graph structure simultaneously. Despite the proliferation of GSL methods developed in recent years, there is no standard experimental setting or fair comparison for performance evaluation, which creates a great obstacle to understanding the progress in this field. To fill this gap, we systematically analyze the performance of GSL in different scenarios and develop a comprehensive Graph Structure Learning Benchmark (GSLB) curated from 20 diverse graph datasets and 16 distinct GSL algorithms. Specifically, GSLB systematically investigates the characteristics of GSL in terms of three dimensions: effectiveness, robustness, and complexity. We comprehensively evaluate state-of-the-art GSL algorithms in node- and graph-level tasks, and analyze their performance in robust learning and model complexity. Further, to facilitate reproducible research, we have developed an easy-to-use library for training, evaluating, and visualizing different GSL methods. Empirical results of our extensive experiments demonstrate the ability of GSL and reveal its potential benefits on various downstream tasks, offering insights and opportunities for future research. The code of GSLB is available at: https://github.com/GSL-Benchmark/GSLB.

We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data satisfying the few root causes assumption, we show superior performance compared to prior DAG learning methods.

Graph-based semi-supervised learning (GSSL) serves as a powerful tool to model the underlying manifold structures of samples in high-dimensional spaces. It involves two phases: constructing an affinity graph from available data and inferring labels for unlabeled nodes on this graph. While numerous algorithms have been developed for label inference, the crucial graph construction phase has received comparatively less attention, despite its significant influence on the subsequent phase. In this paper, we present an optimal asymmetric graph structure for the label inference phase with theoretical motivations. Unlike existing graph construction methods, we differentiate the distinct roles that labeled nodes and unlabeled nodes could play. Accordingly, we design an efficient block-wise graph learning algorithm with a global convergence guarantee. Other benefits induced by our method, such as enhanced robustness to noisy node features, are explored as well. Finally, we perform extensive experiments on synthetic and real-world datasets to demonstrate its superiority to the state-of-the-art graph construction methods in GSSL.

Graph data augmentation has shown superiority in enhancing generalizability and robustness of GNNs in graph-level classifications. However, existing methods primarily focus on the augmentation in the graph signal space and the graph structure space independently, neglecting the joint interaction between them. In this paper, we address this limitation by formulating the problem as an optimal transport problem that aims to find an optimal inter-graph node matching strategy considering the interactions between graph structures and signals. To solve this problem, we propose a novel graph mixup algorithm called FGWMixup, which seeks a "midpoint" of source graphs in the Fused Gromov-Wasserstein (FGW) metric space. To enhance the scalability of our method, we introduce a relaxed FGW solver that accelerates FGWMixup by improving the convergence rate from $\mathcal{O}(t^{-1})$ to $\mathcal{O}(t^{-2})$. Extensive experiments conducted on five datasets using both classic (MPNNs) and advanced (Graphormers) GNN backbones demonstrate that \mname\xspace effectively improves the generalizability and robustness of GNNs. Codes are available at https://github.com/ArthurLeoM/FGWMixup.

In this work, we describe a method that determines an exact map from a finite set of subgraph densities to the parameters of a stochastic block model (SBM) matching these densities. Given a number K of blocks, the subgraph densities of a finite number of stars and bistars uniquely determines a single element of the class of all degree-separated stochastic block models with K blocks. Our method makes it possible to translate estimates of these subgraph densities into model parameters, and hence to use subgraph densities directly for inference. The computational overhead is negligible; computing the translation map is polynomial in K, but independent of the graph size once the subgraph densities are given.

Inverse protein folding is challenging due to its inherent one-to-many mapping characteristic, where numerous possible amino acid sequences can fold into a single, identical protein backbone. This task involves not only identifying viable sequences but also representing the sheer diversity of potential solutions. However, existing discriminative models, such as transformer-based auto-regressive models, struggle to encapsulate the diverse range of plausible solutions. In contrast, diffusion probabilistic models, as an emerging genre of generative approaches, offer the potential to generate a diverse set of sequence candidates for determined protein backbones. We propose a novel graph denoising diffusion model for inverse protein folding, where a given protein backbone guides the diffusion process on the corresponding amino acid residue types. The model infers the joint distribution of amino acids conditioned on the nodes' physiochemical properties and local environment. Moreover, we utilize amino acid replacement matrices for the diffusion forward process, encoding the biologically-meaningful prior knowledge of amino acids from their spatial and sequential neighbors as well as themselves, which reduces the sampling space of the generative process. Our model achieves state-of-the-art performance over a set of popular baseline methods in sequence recovery and exhibits great potential in generating diverse protein sequences for a determined protein backbone structure.

Accurate Urban SpatioTemporal Prediction (USTP) is of great importance to the development and operation of the smart city. As an emerging building block, multi-sourced urban data are usually integrated as urban knowledge graphs (UrbanKGs) to provide critical knowledge for urban spatiotemporal prediction models. However, existing UrbanKGs are often tailored for specific downstream prediction tasks and are not publicly available, which limits the potential advancement. This paper presents UUKG, the unified urban knowledge graph dataset for knowledge-enhanced urban spatiotemporal predictions. Specifically, we first construct UrbanKGs consisting of millions of triplets for two metropolises by connecting heterogeneous urban entities such as administrative boroughs, POIs, and road segments. Moreover, we conduct qualitative and quantitative analysis on constructed UrbanKGs and uncover diverse high-order structural patterns, such as hierarchies and cycles, that can be leveraged to benefit downstream USTP tasks. To validate and facilitate the use of UrbanKGs, we implement and evaluate 15 KG embedding methods on the KG completion task and integrate the learned KG embeddings into 9 spatiotemporal models for five different USTP tasks. The extensive experimental results not only provide benchmarks of knowledge-enhanced USTP models under different task settings but also highlight the potential of state-of-the-art high-order structure-aware UrbanKG embedding methods. We hope the proposed UUKG fosters research on urban knowledge graphs and broad smart city applications. The dataset and source code are available at https://github.com/usail-hkust/UUKG/.

Developing generalizable models that can effectively learn from limited data and with minimal reliance on human supervision is a significant objective within the machine learning community, particularly in the era of deep neural networks. Therefore, to achieve data-efficient learning, researchers typically explore approaches that can leverage more related or unlabeled data without necessitating additional manual labeling efforts, such as Semi-Supervised Learning (SSL), Transfer Learning (TL), and Data Augmentation (DA). SSL leverages unlabeled data in the training process, while TL enables the transfer of expertise from related data distributions. DA broadens the dataset by synthesizing new data from existing examples. However, the significance of additional knowledge contained within labels has been largely overlooked in research. In this paper, we propose a novel perspective on data efficiency that involves exploiting the semantic information contained in the labels of the available data. Specifically, we introduce a Language Semantic Graph (LSG) which is constructed from labels manifest as natural language descriptions. Upon this graph, an auxiliary graph neural network is trained to extract high-level semantic relations and then used to guide the training of the primary model, enabling more adequate utilization of label knowledge. Across image, video, and audio modalities, we utilize the LSG method in both TL and SSL scenarios and illustrate its versatility in significantly enhancing performance compared to other data-efficient learning approaches. Additionally, our in-depth analysis shows that the LSG method also expedites the training process.

Latent graph inference (LGI) aims to jointly learn the underlying graph structure and node representations from data features. However, existing LGI methods commonly suffer from the issue of supervision starvation, where massive edge weights are learned without semantic supervision and do not contribute to the training loss. Consequently, these supervision-starved weights, which determine the predictions of testing samples, cannot be semantically optimal, resulting in poor generalization. In this paper, we observe that this issue is actually caused by the graph sparsification operation, which severely destroys the important connections established between pivotal nodes and labeled ones. To address this, we propose to restore the corrupted affinities and replenish the missed supervision for better LGI. The key challenge then lies in identifying the critical nodes and recovering the corrupted affinities. We begin by defining the pivotal nodes as k-hop starved nodes, which can be identified based on a given adjacency matrix. Considering the high computational burden, we further present a more efficient alternative inspired by CUR matrix decomposition. Subsequently, we eliminate the starved nodes by reconstructing the destroyed connections. Extensive experiments on representative benchmarks demonstrate that reducing the starved nodes consistently improves the performance of state-of-the-art LGI methods, especially under extremely limited supervision (6.12% improvement on Pubmed with a labeling rate of only 0.3%).

Attention mechanisms have made significant strides in graph learning, yet they still exhibit notable limitations: local attention faces challenges in capturing long-range information due to the inherent problems of the message-passing scheme, while global attention cannot reflect the hierarchical neighborhood structure and fails to capture fine-grained local information. In this paper, we propose a novel multi-hop graph attention mechanism, named Subtree Attention (STA), to address the aforementioned issues. STA seamlessly bridges the fully-attentional structure and the rooted subtree, with theoretical proof that STA approximates the global attention under extreme settings. By allowing direct computation of attention weights among multi-hop neighbors, STA mitigates the inherent problems in existing graph attention mechanisms. Further we devise an efficient form for STA by employing kernelized softmax, which yields a linear time complexity. Our resulting GNN architecture, the STAGNN, presents a simple yet performant STA-based graph neural network leveraging a hop-aware attention strategy. Comprehensive evaluations on ten node classification datasets demonstrate that STA-based models outperform existing graph transformers and mainstream GNNs. The code is available at https://github.com/LUMIA-Group/SubTree-Attention.

Graph neural networks (GNNs) have become increasingly popular for classification tasks on graph-structured data. Yet, the interplay between graph topology and feature evolution in GNNs is not well understood. In this paper, we focus on node-wise classification, illustrated with community detection on stochastic block model graphs, and explore the feature evolution through the lens of the "Neural Collapse" (NC) phenomenon. When training instance-wise deep classifiers (e.g. for image classification) beyond the zero training error point, NC demonstrates a reduction in the deepest features' within-class variability and an increased alignment of their class means to certain symmetric structures. We start with an empirical study that shows that a decrease in within-class variability is also prevalent in the node-wise classification setting, however, not to the extent observed in the instance-wise case. Then, we theoretically study this distinction. Specifically, we show that even an "optimistic" mathematical model requires that the graphs obey a strict structural condition in order to possess a minimizer with exact collapse. Furthermore, by studying the gradient dynamics of this model, we provide reasoning for the partial collapse observed empirically. Finally, we present a study on the evolution of within- and between-class feature variability across layers of a well-trained GNN and contrast the behavior with spectral methods.

Combinatorial optimization (CO) problems are often NP-hard and thus out of reach for exact algorithms, making them a tempting domain to apply machine learning methods. The highly structured constraints in these problems can hinder either optimization or sampling directly in the solution space. On the other hand, GFlowNets have recently emerged as a powerful machinery to efficiently sample from composite unnormalized densities sequentially and have the potential to amortize such solution-searching processes in CO, as well as generate diverse solution candidates. In this paper, we design Markov decision processes (MDPs) for different combinatorial problems and propose to train conditional GFlowNets to sample from the solution space. Efficient training techniques are also developed to benefit long-range credit assignment. Through extensive experiments on a variety of different CO tasks with synthetic and realistic data, we demonstrate that GFlowNet policies can efficiently find high-quality solutions. Our implementation is open-sourced at https://github.com/zdhNarsil/GFlowNet-CombOpt.

Self-supervised learning on graph aims to learn graph representations in an unsupervised manner. While graph contrastive learning (GCL - relying on graph augmentation for creating perturbation views of anchor graphs and maximizing/minimizing similarity for positive/negative pairs) is a popular self-supervised method, it faces challenges in finding label-invariant augmented graphs and determining the exact extent of similarity between sample pairs to be achieved. In this work, we propose an alternative self-supervised solution that (i) goes beyond the label invariance assumption without distinguishing between positive/negative samples, (ii) can calibrate the encoder for preserving not only the structural information inside the graph, but the matching information between different graphs, (iii) learns isometric embeddings that preserve the distance between graphs, a by-product of our objective. Motivated by optimal transport theory, this scheme relays on an observation that the optimal transport plans between node representations at the output space, which measure the matching probability between two distributions, should be consistent to the plans between the corresponding graphs at the input space. The experimental findings include: (i) The plan alignment strategy significantly outperforms the counterpart using the transport distance; (ii) The proposed model shows superior performance using only node attributes as calibration signals, without relying on edge information; (iii) Our model maintains robust results even under high perturbation rates; (iv) Extensive experiments on various benchmarks validate the effectiveness of the proposed method.