ICML 2024 Papers

Graph neural networks (GNNs) have exhibited prominent performance in learning graph-structured data. Considering node classification task, based on the i.i.d assumption among node labels, the traditional supervised learning simply sums up cross-entropy losses of the independent training nodes and applies the average loss to optimize GNNs' weights. But different from other data formats, the nodes are naturally connected. It is found that the independent distribution modeling of node labels restricts GNNs' capability to generalize over the entire graph and defend adversarial attacks. In this work, we propose a new framework, termed joint-cluster supervised learning, to model the joint distribution of each node with its corresponding cluster. We learn the joint distribution of node and cluster labels conditioned on their representations, and train GNNs with the obtained joint loss. In this way, the data-label reference signals extracted from the local cluster explicitly strengthen the discrimination ability on the target node. The extensive experiments demonstrate that our joint-cluster supervised learning can effectively bolster GNNs' node classification accuracy. Furthermore, being benefited from the reference signals which may be free from spiteful interference, our learning paradigm significantly protects the node classification from being affected by the adversarial attack.

Graph Contrastive Learning (GCL) has emerged as a highly effective self-supervised approach in graph representation learning. However, prevailing GCL methods confront two primary challenges: 1) They predominantly operate under homophily assumptions, focusing on low-frequency signals in node features while neglecting heterophilic edges that connect nodes with dissimilar features. 2) Their reliance on neighborhood aggregation for inference leads to scalability challenges and hinders deployment in real-time applications. In this paper, we introduce S3GCL, an innovative framework designed to tackle these challenges. Inspired by spectral GNNs, we initially demonstrate the correlation between frequency and homophily levels. Then, we propose a novel cosine-parameterized Chebyshev polynomial as low/high-pass filters to generate biased graph views. To resolve the inference dilemma, we incorporate an MLP encoder and enhance its awareness of graph context by introducing structurally and semantically neighboring nodes as positive pairs in the spatial domain. Finally, we formulate a cross-pass GCL objective between full-pass MLP and biased-pass GNN filtered features, eliminating the need for augmentation. Extensive experiments on real-world tasks validate S3GCL proficiency in generalization to diverse homophily levels and its superior inference efficiency.

A large body of work has investigated the properties of graph neural networks and identified several limitations, particularly pertaining to their expressive power. Their inability to count certain *patterns* (e.g., cycles) in a graph lies at the heart of such limitations, since many functions to be learned rely on the ability of counting such patterns. Two prominent paradigms aim to address this limitation by enriching the graph features with *subgraph* or *homomorphism* pattern counts. In this work, we show that both of these approaches are sub-optimal in a certain sense and argue for a more *fine-grained* approach, which incorporates the homomorphism counts of *all* structures in the ``basis'' of the target pattern. This yields strictly more expressive architectures without incurring any additional overhead in terms of computational complexity compared to existing approaches. We prove a series of theoretical results on node-level and graph-level *motif parameters* and empirically validate them on standard benchmark datasets.

Graph representation learning aims to represent graphs as vectors that can be utilized in downstream tasks such as graph classification. In this work, we focus on learning diverse representations that can capture the graph information as much as possible. We propose quantifying graph information using graph entropy, where we define a probability distribution of a graph based on its nodes' representations and global-graph representation. However, the computation of graph entropy is NP-hard due to the complex vertex-packing polytope involved in its definition. To address this challenge, we provide an approximation method leveraging orthonormal representations for graph entropy maximization. The proposed method is implemented via graph neural networks, resulting in informative node-level and graph-level representations. Experimental results demonstrate the effectiveness of our method in comparison to many baselines in unsupervised learning and semi-supervised learning tasks. The code of our method is available at https://github.com/MathAdventurer/GeMax.

Graph neural networks (GNNs) have advanced the state of the art in various domains. Despite their remarkable success, the uncertainty estimation of GNN predictions remains under-explored, which limits their practical applications especially in risk-sensitive areas. Current works suffer from either intractable posteriors or inflexible prior specifications, leading to sub-optimal empirical results. In this paper, we present graph neural stochastic diffusion (GNSD), a novel framework for estimating predictive uncertainty on graphs by establishing theoretical connections between GNNs and stochastic partial differential equation. GNSD represents a GNN-based parameterization of the proposed graph stochastic diffusion equation which includes a $Q$-Wiener process to model the stochastic evolution of node representations. GNSD introduces a drift network to guarantee accurate prediction and a stochastic forcing network to model the propagation of epistemic uncertainty among nodes. Extensive experiments are conducted on multiple detection tasks, demonstrating that GNSD yields the superior performance over existing strong approaches.

Graph Contrastive Learning (GCL) aims to learn node representations by aligning positive pairs and separating negative ones. However, few of researchers have focused on the inner law behind specific augmentations used in graph-based learning. What kind of augmentation will help downstream performance, how does contrastive learning actually influence downstream tasks, and why the magnitude of augmentation matters so much? This paper seeks to address these questions by establishing a connection between augmentation and downstream performance. Our findings reveal that GCL contributes to downstream tasks mainly by separating different classes rather than gathering nodes of the same class. So perfect alignment and augmentation overlap which draw all intra-class samples the same can not fully explain the success of contrastive learning. Therefore, in order to understand how augmentation aids the contrastive learning process, we conduct further investigations into the generalization, finding that perfect alignment that draw positive pair the same could help contrastive loss but is poisonous to generalization, as a result, perfect alignment may not lead to best downstream performance, so specifically designed augmentation is needed to achieve appropriate alignment performance and improve downstream accuracy. We further analyse the result by information theory and graph spectrum theory and propose two simple but effective methods to verify the theories. The two methods could be easily applied to various GCL algorithms and extensive experiments are conducted to prove its effectiveness. The code is available at https://github.com/somebodyhh1/GRACEIS

Equivariant Graph Neural Networks (GNNs) have made remarkable success in a variety of scientific applications. However, existing equivariant GNNs encounter the efficiency issue for large geometric graphs and perform poorly if the input is reduced to sparse local graph for speed acceleration. In this paper, we propose FastEGNN, an enhanced model of equivariant GNNs on large geometric graphs. The central idea is leveraging a small ordered set of virtual nodes to approximate the large unordered graph of real nodes. In particular, we distinguish the message passing and aggregation for different virtual node to encourage the mutual distinctiveness, and minimize the Maximum Mean Discrepancy (MMD) between virtual and real coordinates to realize the global distributedness. FastEGNN meets all necessary E(3) symmetries, with certain universal expressivity assurance as well. Our experiments on N-body systems (100 nodes), proteins (800 nodes) and water-3D (8000 nodes), demonstrate that FastEGNN achieves a promising balance between accuracy and efficiency, and outperforms EGNN in accuracy even after dropping all edges in real systems like proteins and water-3D.

Permutation equivariant neural networks are typically used to learn from data that lives on a graph. However, for any graph $G$ that has $n$ vertices, using the symmetric group $S_n$ as its group of symmetries does not take into account the relations that exist between the vertices. Given that the actual group of symmetries is the automorphism group Aut$(G)$, we show how to construct neural networks that are equivariant to Aut$(G)$ by obtaining a full characterisation of the learnable, linear, Aut$(G)$-equivariant functions between layers that are some tensor power of $\mathbb{R}^{n}$. In particular, we find a spanning set of matrices for these layer functions in the standard basis of $\mathbb{R}^{n}$. This result has important consequences for learning from data whose group of symmetries is a finite group because a theorem by Frucht (1938) showed that any finite group is isomorphic to the automorphism group of a graph.

The distinguishing power of graph transformers is tied to the choice of *positional encoding*: features used to augment the base transformer with information about the graph. There are two primary types of positional encoding: *absolute positional encodings (APEs)* and *relative positional encodings (RPEs)*. APEs assign features to each node and are given as input to the transformer. RPEs instead assign a feature to each *pair of nodes*, e.g., shortest-path distance, and are used to augment the attention block. A priori, it is unclear which method is better for maximizing the power of the resulting graph transformer. In this paper, we aim to understand the relationship between these different types of positional encodings. Interestingly, we show that graph transformers using APEs and RPEs are equivalent in their ability to distinguish non-isomorphic graphs. In particular, we demonstrate how to interchange APEs and RPEs while maintaining their distinguishing power in terms of graph transformers. However, in the case of graphs with node features, we show that RPEs may have an advantage over APEs. Based on our theoretical results, we provide a study of different APEs and RPEs---including the shortest-path and resistance distance and the recently introduced stable and expressive positional encoding (SPE)---and compare their distinguishing power in terms of transformers. We believe our work will help navigate the vast number of positional encoding choices and provide guidance on the future design of positional encodings for graph transformers.

Understanding the interactions and interplay of microorganisms is a great challenge with many applications in medical and environmental settings. In this work, we model bacterial communities directly from their genomes using graph neural networks (GNNs). GNNs leverage the inductive bias induced by the set nature of bacteria, enforcing permutation invariance and granting combinatorial generalization. We propose to learn the dynamics implicitly by directly predicting community relative abundance profiles at steady state, thus escaping the need for growth curves. On two real-world datasets, we show for the first time generalization to unseen bacteria and different community structures. To investigate the prediction results more deeply, we create a simulation for flexible data generation and analyze effects of bacteria interaction strength, community size, and training data amount.

GNNs rely on the exchange of messages to distribute information along the edges of the graph. This approach makes the efficiency of architectures highly dependent on the specific structure of the input graph. Certain graph topologies lead to inefficient information propagation, resulting in a phenomenon known as over-squashing. While the majority of existing methods address over-squashing by rewiring the input graph, our novel approach involves constructing a graph directly from features using Delaunay Triangulation. We posit that the topological properties of the resulting graph prove advantageous for mitigate oversmoothing and over-squashing. Our extensive experimentation demonstrates that our method consistently outperforms established graph rewiring methods.

Graph Transformer, due to its global attention mechanism, has emerged as a new tool in dealing with graph-structured data. It is well recognized that the global attention mechanism considers a wider receptive field in a fully connected graph, leading many to believe that useful information can be extracted from all the nodes. In this paper, we challenge this belief: does the globalizing property always benefit Graph Transformers? We reveal the over-globalizing problem in Graph Transformer by presenting both empirical evidence and theoretical analysis, i.e., the current attention mechanism overly focuses on those distant nodes, while the near nodes, which actually contain most of the useful information, are relatively weakened. Then we propose a novel Bi-Level Global Graph Transformer with Collaborative Training (CoBFormer), including the inter-cluster and intra-cluster Transformers, to prevent the over-globalizing problem while keeping the ability to extract valuable information from distant nodes. Moreover, the collaborative training is proposed to improve the model's generalization ability with a theoretical guarantee. Extensive experiments on various graphs well validate the effectiveness of our proposed CoBFormer.

Recently, there has been a surge of interest in developing graph neural networks that utilize the invariance principle on graphs to generalize the out-of-distribution (OOD) data. Due to the limited knowledge about OOD data, existing approaches often pose assumptions about the correlation strengths of the underlying spurious features and the target labels. However, this prior is often unavailable and will change arbitrarily in the real-world scenarios, which may lead to severe failures of the existing graph invariance learning methods. To bridge this gap, we introduce a novel graph invariance learning paradigm, which induces a robust and general inductive bias, which is built upon the observation that the infomax principle encourages learning spurious features regardless of spurious correlation strengths. We further propose the EQuAD framework that realizes this learning paradigm and employs tailored learning objectives that provably elicit invariant features by disentangling them from the spurious features learned through infomax. Notably, EQuAD shows stable and enhanced performance across different degrees of bias in synthetic datasets and challenging real-world datasets up to 31.76%.

Graph matching in the setting of federated learning is still an open problem. This paper proposes an unsupervised federated graph matching algorithm, UFGM, for inferring matched node pairs on different graphs across clients while maintaining privacy requirement, by leveraging graphlet theory and trust region optimization. First, the nodes' graphlet features are captured to generate pseudo matched node pairs on different graphs across clients as pseudo training data for tackling the dilemma of unsupervised graph matching in federated setting and leveraging the strength of supervised graph matching. An approximate graphlet enumeration method is proposed to sample a small number of graphlets and capture nodes' graphlet features. Theoretical analysis is conducted to demonstrate that the approximate method is able to maintain the quality of graphlet estimation while reducing its expensive cost. Second, we propose a separate trust region algorithm for pseudo supervised federated graph matching while maintaining the privacy constraints. In order to avoid expensive cost of the second-order Hessian computation in the trust region algorithm, we propose two weak quasi-Newton conditions to construct a positive definite scalar matrix as the Hessian approximation with only first-order gradients. We theoretically derive the error introduced by the separate trust region due to the Hessian approximation and conduct the convergence analysis of the approximation method.

Explainable Graph Neural Network (GNN) has emerged recently to foster the trust of using GNNs. Existing GNN explainers are developed from various perspectives to enhance the explanation performance. We take the first step to study GNN explainers under adversarial attack—We found that an adversary slightly perturbing graph structure can ensure GNN model makes correct predictions, but the GNN explainer yields a drastically different explanation on the perturbed graph. Specifically, we first formulate the attack problem under a practical threat model (i.e., the adversary has limited knowledge about the GNN explainer and a restricted perturbation budget). We then design two methods (i.e., one is loss-based and the other is deduction-based) to realize the attack. We evaluate our attacks on various GNN explainers and the results show these explainers are fragile.

Class imbalance is prevalent in real-world node classification tasks and poses great challenges for graph learning models. Most existing studies are rooted in a class-rebalancing (CR) perspective and address class imbalance with class-wise reweighting or resampling. In this work, we approach the root cause of class-imbalance bias from an topological paradigm. Specifically, we theoretically reveal two **fundamental phenomena in the graph topology** that greatly exacerbate the predictive bias stemming from class imbalance. On this basis, we devise a lightweight topological augmentation framework BAT to mitigate the class-imbalance bias without class rebalancing. Being orthogonal to CR, BAT can function as an **efficient plug-and-play module** that can be seamlessly combined with and significantly boost existing CR techniques. Systematic experiments on real-world imbalanced graph learning tasks show that BAT can deliver up to 46.27% performance gain and up to 72.74% bias reduction over existing techniques. Code, examples, and documentations are available at https://github.com/ZhiningLiu1998/BAT.

Graph Neural Networks (GNNs) have become a building block in graph data processing, with wide applications in critical domains. The growing needs to deploy GNNs in high-stakes applications necessitate explainability for users in the decision-making processes. A popular paradigm for the explainability of GNNs is to identify explainable subgraphs by comparing their labels with the ones of original graphs. This task is challenging due to the substantial distributional shift from the original graphs in the training set to the set of explainable subgraphs, which prevents accurate prediction of labels with the subgraphs. To address it, in this paper, we propose a novel method that generates proxy graphs for explainable subgraphs that are in the distribution of training data. We introduce a parametric method that employs graph generators to produce proxy graphs. A new training objective based on information theory is designed to ensure that proxy graphs not only adhere to the distribution of training data but also preserve explanatory factors. Such generated proxy graphs can be reliably used to approximate the predictions of the labels of explainable subgraphs. Empirical evaluations across various datasets demonstrate our method achieves more accurate explanations for GNNs.

Incorporating spectral information to enhance Graph Neural Networks (GNNs) has shown promising results but raises a fundamental challenge due to the inherent ambiguity of eigenvectors. Various architectures have been proposed to address this ambiguity, referred to as spectral invariant architectures. Notable examples include GNNs and Graph Transformers that use spectral distances, spectral projection matrices, or other invariant spectral features. However, the potential expressive power of these spectral invariant architectures remains largely unclear. The goal of this work is to gain a deep theoretical understanding of the expressive power obtainable when using spectral features. We first introduce a novel message-passing framework for designing spectral invariant GNNs, called Eigenspace Projection GNN (EPNN). Our comprehensive analysis shows that EPNN essentially unifies all prior spectral invariant architectures, in that they are either strictly less expressive or equivalent to EPNN. A fine-grained expressiveness hierarchy among different architectures is also established. On the other hand, we present a surprising result that EPNN itself is bounded by a recently proposed class of Subgraph GNNs, implying that all these spectral invariant architectures are strictly less expressive than 3-WL. Finally, we demonstrate that these spectral features offer no additional advantage when combined with more expressive GNNs.

In network games, individuals interact strategically within network environments to maximize their utilities. However, obtaining network structures is challenging. In this work, we propose an unsupervised learning model, called data-dependent gated-prior graph variational autoencoder (GPGVAE), that infers the underlying latent interaction type (strategic complement vs. substitute) among individuals and the latent network structure based on their observed actions. Specially, we propose a spectral graph neural network (GNN) based encoder to predict the interaction type and a data-dependent gated prior that models network structures conditioned on the interaction type. We further propose a Transformer based mixture of Bernoulli encoder of network structures and a GNN based decoder of game actions. We systematically study the Monte Carlo gradient estimation methods and effectively train our model in a stage-wise fashion. Extensive experiments across various synthetic and real-world network games demonstrate that our model achieves state-of-the-art performances in inferring network structures and well captures interaction types.