Graph learning tasks often hinge on identifying key substructure patterns -- such as triadic closures in social networks or benzene rings in molecular graphs -- that underpin downstream performance. However, most existing graph neural networks (GNNs) rely on message passing, which aggregates local neighborhood information iteratively and struggles to explicitly capture such fundamental motifs, like triangles, k-cliques, and rings. This limitation hinders both expressiveness and long-range dependency modeling. In this paper, we introduce the Neural Graph Pattern Machine (GPM), a novel framework that bypasses message passing by learning directly from graph substructures. GPM efficiently extracts, encodes, and prioritizes task-relevant graph patterns, offering greater expressivity and improved ability to capture long-range dependencies. Empirical evaluations across four standard tasks -- node classification, link prediction, graph classification, and graph regression -- demonstrate that GPM outperforms state-of-the-art baselines. Further analysis reveals that GPM exhibits strong out-of-distribution generalization, desirable scalability, and enhanced interpretability. Code and datasets are available at: https://github.com/Zehong-Wang/GPM.
We study the effectiveness of molecular fingerprints for peptide property prediction and demonstrate that domain-specific feature extraction from molecular graphs can outperform complex and computationally expensive models such as GNNs, pretrained sequence-based transformers and multimodal ensembles, even without hyperparameter tuning. To this end, we perform a thorough evaluation on 126 datasets, achieving state-of-the-art results on LRGB and 5 other peptide function prediction benchmarks. We show that models based on count variants of ECFP, Topological Torsion, and RDKit molecular fingerprints and LightGBM as classification head are remarkably robust. The strong performance of molecular fingerprints, which are intrinsically very short-range feature encoders, challenges the presumed importance of long-range interactions in peptides. Our conclusion is that the use of molecular fingerprints for larger molecules, such as peptides, can be a computationally feasible, low-parameter, and versatile alternative to sophisticated deep learning models.
The pre-train then fine-tune approach has advanced GNNs by enabling general knowledge capture without task-specific labels. However, an objective gap between pre-training and downstream tasks limits its effectiveness. Recent graph prompting methods aim to close this gap through task reformulations and learnable prompts. Despite this, they struggle with complex graphs like heterophily graphs. Freezing the GNN encoder can reduce the impact of prompting, while simple prompts fail to handle diverse hop-level distributions. This paper identifies two key challenges in adapting graph prompting methods for complex graphs: (1) adapting the model to new distributions in downstream tasks to mitigate pre-training and fine-tuning discrepancies from heterophily and (2) customizing prompts for hop-specific node requirements. To overcome these challenges, we propose Distribution-aware Graph Prompt Tuning (DAGPrompT), which integrates a GLoRA module for optimizing the GNN encoder's projection matrix and message-passing schema through low-rank adaptation. DAGPrompT also incorporates hop-specific prompts accounting for varying graph structures and distributions among hops. Evaluations on 10 datasets and 14 baselines demonstrate that DAGPrompT improves accuracy by up to 4.79 in node and graph classification tasks, setting a new state-of-the-art while preserving efficiency. Codes are available at GitHub.
Invariant learning demonstrates substantial potential for enhancing the generalization of graph neural networks (GNNs) with out-of-distribution (OOD) data. It aims to recognize stable features in graph data for classification, based on the premise that these features causally determine the target label, and their influence is invariant to changes in distribution. Along this line, most studies have attempted to pinpoint these stable features by emphasizing explicit substructures in the graph, such as masked or attentive subgraphs, and primarily enforcing the invariance principle in the semantic space, i.e., graph representations. However, we argue that focusing only on the semantic space may not accurately identify these stable features. To address this, we introduce the Unified Invariant Learning (UIL) framework for graph classification. It provides a unified perspective on invariant graph learning, emphasizing both structural and semantic invariance principles to identify more robust stable features. In the graph space, UIL adheres to the structural invariance principle by reducing the distance between graphons over a set of stable features across different environments. Simultaneously, to confirm semantic invariance, UIL underscores that the acquired graph representations should demonstrate exemplary performance across diverse environments. We present both theoretical and empirical evidence to confirm our method's ability to recognize superior stable features. Moreover, through a series of comprehensive experiments complemented by in-depth analyses, we demonstrate that UIL considerably enhances OOD generalization, surpassing the performance of leading baseline methods. Our codes are available at https://github.com/yongduosui/UIL.
Despite significant advancements in causal research on graphs and its application to cracking label imbalance, the role of edge features in detecting the causal effects within graphs has been largely overlooked, leaving existing methods with untapped potential for further performance gains. In this paper, we enhance the causal attention mechanism through effectively leveraging edge information to disentangle the causal subgraph from the original graph, as well as further utilizing edge features to reshape graph representations. Capturing more comprehensive causal signals, our design leads to improved performance on graph classification tasks with label imbalance issues. We evaluate our approach on real-word datasets PTC, Tox21, and ogbg-molhiv, observing improvements over baselines. Overall, we highlight the importance of edge features in graph causal detection and provide a promising direction for addressing label imbalance challenges in graph-level tasks. The model implementation details and the codes are available on https://github.com/fengrui-z/ECAL
While message passing graph neural networks result in informative node embeddings, they may suffer from describing the topological properties of graphs. To this end, node filtration has been widely used as an attempt to obtain the topological information of a graph using persistence diagrams. However, these attempts have faced the problem of losing node embedding information, which in turn prevents them from providing a more expressive graph representation. To tackle this issue, we shift our focus to edge filtration and introduce a novel edge filtration-based persistence diagram, named Topological Edge Diagram (TED), which is mathematically proven to preserve node embedding information as well as contain additional topological information. To implement TED, we propose a neural network based algorithm, named Line Graph Vietoris-Rips (LGVR) Persistence Diagram, that extracts edge information by transforming a graph into its line graph. Through LGVR, we propose two model frameworks that can be applied to any message passing GNNs, and prove that they are strictly more powerful than Weisfeiler-Lehman type colorings. Finally we empirically validate superior performance of our models on several graph classification and regression benchmarks.
This study aims to build a pre-trained Graph Neural Network (GNN) model on molecules without human annotations or prior knowledge. Although various attempts have been proposed to overcome limitations in acquiring labeled molecules, the previous pre-training methods still rely on semantic subgraphs, i.e., functional groups. Only focusing on the functional groups could overlook the graph-level distinctions. The key challenge to build a pre-trained GNN on molecules is how to (1) generate well-distinguished graph-level representations and (2) automatically discover the functional groups without prior knowledge. To solve it, we propose a novel Subgraph-conditioned Graph Information Bottleneck, named S-CGIB, for pre-training GNNs to recognize core subgraphs (graph cores) and significant subgraphs. The main idea is that the graph cores contain compressed and sufficient information that could generate well-distinguished graph-level representations and reconstruct the input graph conditioned on significant subgraphs across molecules under the S-CGIB principle. To discover significant subgraphs without prior knowledge about functional groups, we propose generating a set of functional group candidates, i.e., ego networks, and using an attention-based interaction between the graph core and the candidates. Despite being identified from self-supervised learning, our learned subgraphs match the real-world functional groups. Extensive experiments on molecule datasets across various domains demonstrate the superiority of S-CGIB.
Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present a semi-implicit neural ODE approach that exploits the partitionable structure of the underlying dynamics. Our technique leads to an implicit neural network with significant computational advantages over existing approaches because of enhanced stability and efficient linear solves during time integration. We show that our approach outperforms existing approaches on a variety of applications including graph classification and learning complex dynamical systems. We also demonstrate that our approach can train challenging neural ODEs where both explicit methods and fully implicit methods are intractable.
Graph Neural Networks (GNNs) have demonstrated their effectiveness in various graph learning tasks, yet their reliance on neighborhood aggregation during inference poses challenges for deployment in latency-sensitive applications, such as real-time financial fraud detection. To address this limitation, recent studies have proposed distilling knowledge from teacher GNNs into student Multi-Layer Perceptrons (MLPs) trained on node content, aiming to accelerate inference. However, these approaches often inadequately explore structural information when inferring unseen nodes. To this end, we introduce SimMLP, a Self-supervised framework for learning MLPs on graphs, designed to fully integrate rich structural information into MLPs. Notably, SimMLP is the first MLP-learning method that can achieve equivalence to GNNs in the optimal case. The key idea is to employ self-supervised learning to align the representations encoded by graph context-aware GNNs and neighborhood dependency-free MLPs, thereby fully integrating the structural information into MLPs. We provide a comprehensive theoretical analysis, demonstrating the equivalence between SimMLP and GNNs based on mutual information and inductive bias, highlighting SimMLP's advanced structural learning capabilities. Additionally, we conduct extensive experiments on 20 benchmark datasets, covering node classification, link prediction, and graph classification, to showcase SimMLP's superiority over state-of-the-art baselines, particularly in scenarios involving unseen nodes (e.g., inductive and cold-start node classification) where structural insights are crucial. Our codes are available at: https://github.com/Zehong-Wang/SimMLP.
Graph Transformers (GTs) have demonstrated remarkable performance in incorporating various graph structure information, e.g., long-range structural dependency, into graph representation learning. However, self-attention -- the core module of GTs -- preserves only low-frequency signals on graph features, retaining only homophilic patterns that capture similar features among the connected nodes. Consequently, it has insufficient capacity in modeling complex node label patterns, such as the opposite of homophilic patterns -- heterophilic patterns. Some improved GTs deal with the problem by learning polynomial filters or performing self-attention over the first-order graph spectrum. However, these GTs either ignore rich information contained in the whole spectrum or neglect higher-order spectrum information, resulting in limited flexibility and frequency response in their spectral filters. To tackle these challenges, we propose a novel GT network, namely Graph Fourier Kolmogorov-Arnold Transformers (GrokFormer), to go beyond the self-attention in GTs. GrokFormer leverages learnable activation functions in order-$K$ graph spectrum through Fourier series modeling to i) learn eigenvalue-targeted filter functions producing learnable base that can capture a broad range of frequency signals flexibly, and ii) extract first- and higher-order graph spectral information adaptively. In doing so, GrokFormer can effectively capture intricate patterns hidden across different orders and levels of frequency signals, learning expressive, order-and-frequency-adaptive graph representations. Comprehensive experiments conducted on 10 node classification datasets across various domains, scales, and levels of graph heterophily, as well as 5 graph classification datasets, demonstrate that GrokFormer outperforms state-of-the-art GTs and other advanced graph neural networks.
Leveraging the diversity and quantity of data provided by various graph-structured data augmentations while preserving intrinsic semantic information is challenging. Additionally, successive layers in graph neural network (GNN) tend to produce more similar node embeddings, while graph contrastive learning aims to increase the dissimilarity between negative pairs of node embeddings. This inevitably results in a conflict between the message-passing mechanism (MPM) of GNNs and the contrastive learning (CL) of negative pairs via intraviews. In this paper, we propose a conditional distribution learning (CDL) method that learns graph representations from graph-structured data for semisupervised graph classification. Specifically, we present an end-to-end graph representation learning model to align the conditional distributions of weakly and strongly augmented features over the original features. This alignment enables the CDL model to effectively preserve intrinsic semantic information when both weak and strong augmentations are applied to graph-structured data. To avoid the conflict between the MPM and the CL of negative pairs, positive pairs of node representations are retained for measuring the similarity between the original features and the corresponding weakly augmented features. Extensive experiments with several benchmark graph datasets demonstrate the effectiveness of the proposed CDL method.
Graph Neural Networks (GNNs) are powerful models that can manage complex data sources and their interconnection links. One of GNNs' main drawbacks is their lack of interpretability, which limits their application in sensitive fields. In this paper, we introduce a new methodology involving graph communities to address the interpretability of graph classification problems. The proposed method, called GECo, exploits the idea that if a community is a subset of graph nodes densely connected, this property should play a role in graph classification. This is reasonable, especially if we consider the message-passing mechanism, which is the basic mechanism of GNNs. GECo analyzes the contribution to the classification result of the communities in the graph, building a mask that highlights graph-relevant structures. GECo is tested for Graph Convolutional Networks on six artificial and four real-world graph datasets and is compared to the main explainability methods such as PGMExplainer, PGExplainer, GNNExplainer, and SubgraphX using four different metrics. The obtained results outperform the other methods for artificial graph datasets and most real-world datasets.
Message passing plays a vital role in graph neural networks (GNNs) for effective feature learning. However, the over-reliance on input topology diminishes the efficacy of message passing and restricts the ability of GNNs. Despite efforts to mitigate the reliance, existing study encounters message-passing bottlenecks or high computational expense problems, which invokes the demands for flexible message passing with low complexity. In this paper, we propose a novel dynamic message-passing mechanism for GNNs. It projects graph nodes and learnable pseudo nodes into a common space with measurable spatial relations between them. With nodes moving in the space, their evolving relations facilitate flexible pathway construction for a dynamic message-passing process. Associating pseudo nodes to input graphs with their measured relations, graph nodes can communicate with each other intermediately through pseudo nodes under linear complexity. We further develop a GNN model named $\mathtt{\mathbf{N^2}}$ based on our dynamic message-passing mechanism. $\mathtt{\mathbf{N^2}}$ employs a single recurrent layer to recursively generate the displacements of nodes and construct optimal dynamic pathways. Evaluation on eighteen benchmarks demonstrates the superior performance of $\mathtt{\mathbf{N^2}}$ over popular GNNs. $\mathtt{\mathbf{N^2}}$ successfully scales to large-scale benchmarks and requires significantly fewer parameters for graph classification with the shared recurrent layer.
Graph Neural Networks (GNNs) have become essential in interpreting relational data across various domains, yet, they often struggle to generalize to unseen graph data that differs markedly from training instances. In this paper, we introduce a novel framework called General Retrieval-Augmented Graph Learning (RAGraph), which brings external graph data into the general graph foundation model to improve model generalization on unseen scenarios. On the top of our framework is a toy graph vector library that we established, which captures key attributes, such as features and task-specific label information. During inference, the RAGraph adeptly retrieves similar toy graphs based on key similarities in downstream tasks, integrating the retrieved data to enrich the learning context via the message-passing prompting mechanism. Our extensive experimental evaluations demonstrate that RAGraph significantly outperforms state-of-the-art graph learning methods in multiple tasks such as node classification, link prediction, and graph classification across both dynamic and static datasets. Furthermore, extensive testing confirms that RAGraph consistently maintains high performance without the need for task-specific fine-tuning, highlighting its adaptability, robustness, and broad applicability.
Graph Neural Networks (GNNs) have emerged as a dominant approach in graph representation learning, yet they often struggle to capture consistent similarity relationships among graphs. While graph kernel methods such as the Weisfeiler-Lehman subtree (WL-subtree) and Weisfeiler-Lehman optimal assignment (WLOA) kernels are effective in capturing similarity relationships, they rely heavily on predefined kernels and lack sufficient non-linearity for more complex data patterns. Our work aims to bridge the gap between neural network methods and kernel approaches by enabling GNNs to consistently capture relational structures in their learned representations. Given the analogy between the message-passing process of GNNs and WL algorithms, we thoroughly compare and analyze the properties of WL-subtree and WLOA kernels. We find that the similarities captured by WLOA at different iterations are asymptotically consistent, ensuring that similar graphs remain similar in subsequent iterations, thereby leading to superior performance over the WL-subtree kernel. Inspired by these findings, we conjecture that the consistency in the similarities of graph representations across GNN layers is crucial in capturing relational structures and enhancing graph classification performance. Thus, we propose a loss to enforce the similarity of graph representations to be consistent across different layers. Our empirical analysis verifies our conjecture and shows that our proposed consistency loss can significantly enhance graph classification performance across several GNN backbones on various datasets.
Graph classification in medical imaging and drug discovery requires accuracy and robust uncertainty quantification. To address this need, we introduce Conditional Prediction ROC (CP-ROC) bands, offering uncertainty quantification for ROC curves and robustness to distributional shifts in test data. Although developed for Tensorized Graph Neural Networks (TGNNs), CP-ROC is adaptable to general Graph Neural Networks (GNNs) and other machine learning models. We establish statistically guaranteed coverage for CP-ROC under a local exchangeability condition. This addresses uncertainty challenges for ROC curves under non-iid setting, ensuring reliability when test graph distributions differ from training data. Empirically, to establish local exchangeability for TGNNs, we introduce a data-driven approach to construct local calibration sets for graphs. Comprehensive evaluations show that CP-ROC significantly improves prediction reliability across diverse tasks. This method enhances uncertainty quantification efficiency and reliability for ROC curves, proving valuable for real-world applications with non-iid objects.
Scalability of Graph Neural Networks (GNNs) remains a significant challenge, particularly when dealing with large-scale graphs. To tackle this, coarsening-based methods are used to reduce the graph into a smaller graph, resulting in faster computation. Nonetheless, prior research has not adequately addressed the computational costs during the inference phase. This paper presents a novel approach to improve the scalability of GNNs by reducing computational burden during both training and inference phases. We demonstrate two different methods (Extra-Nodes and Cluster-Nodes). Our study also proposes a unique application of the coarsening algorithm for graph-level tasks, including graph classification and graph regression, which have not yet been explored. We conduct extensive experiments on multiple benchmark datasets in the order of $100K$ nodes to evaluate the performance of our approach. The results demonstrate that our method achieves competitive performance in tasks involving classification and regression on nodes and graphs, compared to traditional GNNs, while having single-node inference times that are orders of magnitude faster. Furthermore, our approach significantly reduces memory consumption, allowing training and inference on low-resource devices where traditional methods struggle.
Graph contrastive learning (GCL) has emerged as a promising approach to enhance graph neural networks' (GNNs) ability to learn rich representations from unlabeled graph-structured data. However, current GCL models face challenges with computational demands and limited feature utilization, often relying only on basic graph properties like node degrees and edge attributes. This constrains their capacity to fully capture the complex topological characteristics of real-world phenomena represented by graphs. To address these limitations, we propose Tensor-Fused Multi-View Graph Contrastive Learning (TensorMV-GCL), a novel framework that integrates extended persistent homology (EPH) with GCL representations and facilitates multi-scale feature extraction. Our approach uniquely employs tensor aggregation and compression to fuse information from graph and topological features obtained from multiple augmented views of the same graph. By incorporating tensor concatenation and contraction modules, we reduce computational overhead by separating feature tensor aggregation and transformation. Furthermore, we enhance the quality of learned topological features and model robustness through noise-injected EPH. Experiments on molecular, bioinformatic, and social network datasets demonstrate TensorMV-GCL's superiority, outperforming 15 state-of-the-art methods in graph classification tasks across 9 out of 11 benchmarks while achieving comparable results on the remaining two. The code for this paper is publicly available at https://github.com/CS-SAIL/Tensor-MV-GCL.git.
Graph representation learning (GRL), enhanced by graph augmentation methods, has emerged as an effective technique achieving performance improvements in wide tasks such as node classification and graph classification. In self-supervised GRL, paired graph augmentations are generated from each graph. Its objective is to infer similar representations for augmentations of the same graph, but maximally distinguishable representations for augmentations of different graphs. Analogous to image and language domains, the desiderata of an ideal augmentation method include both (1) semantics-preservation; and (2) data-perturbation; i.e., an augmented graph should preserve the semantics of its original graph while carrying sufficient variance. However, most existing (un-)/self-supervised GRL methods focus on data perturbation but largely neglect semantics preservation. To address this challenge, in this paper, we propose a novel method, Explanation-Preserving Augmentation (EPA), that leverages graph explanation techniques for generating augmented graphs that can bridge the gap between semantics-preservation and data-perturbation. EPA first uses a small number of labels to train a graph explainer to infer the sub-structures (explanations) that are most relevant to a graph's semantics. These explanations are then used to generate semantics-preserving augmentations for self-supervised GRL, namely EPA-GRL. We demonstrate theoretically, using an analytical example, and through extensive experiments on a variety of benchmark datasets that EPA-GRL outperforms the state-of-the-art (SOTA) GRL methods, which are built upon semantics-agnostic data augmentations.
Glycans are the most complex biological sequence, with monosaccharides forming extended, non-linear sequences. As post-translational modifications, they modulate protein structure, function, and interactions. Due to their diversity and complexity, predictive models of glycan properties and functions are still insufficient. Graph Neural Networks (GNNs) are deep learning models designed to process and analyze graph-structured data. These architectures leverage the connectivity and relational information in graphs to learn effective representations of nodes, edges, and entire graphs. Iteratively aggregating information from neighboring nodes, GNNs capture complex patterns within graph data, making them particularly well-suited for tasks such as link prediction or graph classification across domains. This work presents a new model architecture based on combinatorial complexes and higher-order message passing to extract features from glycan structures into a latent space representation. The architecture is evaluated on an improved GlycanML benchmark suite, establishing a new state-of-the-art performance. We envision that these improvements will spur further advances in computational glycosciences and reveal the roles of glycans in biology.