Graph neural networks based on message-passing mechanisms have achieved advanced results in graph classification tasks. However, their generalization performance degrades when noisy labels are present in the training data. Most existing noisy labeling approaches focus on the visual domain or graph node classification tasks and analyze the impact of noisy labels only from a utility perspective. Unlike existing work, in this paper, we measure the effects of noise labels on graph classification from data privacy and model utility perspectives. We find that noise labels degrade the model's generalization performance and enhance the ability of membership inference attacks on graph data privacy. To this end, we propose the robust graph neural network approach with noisy labeled graph classification. Specifically, we first accurately filter the noisy samples by high-confidence samples and the first feature principal component vector of each class. Then, the robust principal component vectors and the model output under data augmentation are utilized to achieve noise label correction guided by dual spatial information. Finally, supervised graph contrastive learning is introduced to enhance the embedding quality of the model and protect the privacy of the training graph data. The utility and privacy of the proposed method are validated by comparing twelve different methods on eight real graph classification datasets. Compared with the state-of-the-art methods, the RGLC method achieves at most and at least 7.8% and 0.8% performance gain at 30% noisy labeling rate, respectively, and reduces the accuracy of privacy attacks to below 60%.
Graph Neural Networks (GNNs) have become invaluable intellectual property in graph-based machine learning. However, their vulnerability to model stealing attacks when deployed within Machine Learning as a Service (MLaaS) necessitates robust Ownership Demonstration (OD) techniques. Watermarking is a promising OD framework for Deep Neural Networks, but existing methods fail to generalize to GNNs due to the non-Euclidean nature of graph data. Previous works on GNN watermarking have primarily focused on node and graph classification, overlooking Link Prediction (LP). In this paper, we propose GENIE (watermarking Graph nEural Networks for lInk prEdiction), the first-ever scheme to watermark GNNs for LP. GENIE creates a novel backdoor for both node-representation and subgraph-based LP methods, utilizing a unique trigger set and a secret watermark vector. Our OD scheme is equipped with Dynamic Watermark Thresholding (DWT), ensuring high verification probability (>99.99%) while addressing practical issues in existing watermarking schemes. We extensively evaluate GENIE across 4 model architectures (i.e., SEAL, GCN, GraphSAGE and NeoGNN) and 7 real-world datasets. Furthermore, we validate the robustness of GENIE against 11 state-of-the-art watermark removal techniques and 3 model extraction attacks. We also show GENIE's resilience against ownership piracy attacks. Finally, we discuss a defense strategy to counter adaptive attacks against GENIE.
Graph Neural Networks (GNNs) achieve outstanding performance across graph-based tasks but remain difficult to interpret. In this paper, we revisit foundational assumptions underlying model-level explanation methods for GNNs, namely: (1) maximizing classification confidence yields representative explanations, (2) a single explanation suffices for an entire class of graphs, and (3) explanations are inherently trustworthy. We identify pitfalls resulting from these assumptions: methods that optimize for classification confidence may overlook partially learned patterns; topological diversity across graph subsets within the same class is often underrepresented; and explanations alone offer limited support for building user trust when applied to new datasets or models. This paper introduces GNNAnatomy, a distillation-based method designed to generate explanations while avoiding these pitfalls. GNNAnatomy first characterizes graph topology using graphlets, a set of fundamental substructures. We then train a transparent multilayer perceptron surrogate to directly approximate GNN predictions based on the graphlet representations. By analyzing the weights assigned to each graphlet, we identify the most discriminative topologies, which serve as GNN explanations. To account for structural diversity within a class, GNNAnatomy generates explanations at the required granularity through an interface that supports human-AI teaming. This interface helps users identify subsets of graphs where distinct critical substructures drive class differentiation, enabling multi-grained explanations. Additionally, by enabling exploration and linking explanations back to input graphs, the interface fosters greater transparency and trust. We evaluate GNNAnatomy on both synthetic and real-world datasets through quantitative metrics and qualitative comparisons with state-of-the-art model-level explainable GNN methods.
Recent research in the field of graph neural network (GNN) has identified a critical issue known as "over-squashing," resulting from the bottleneck phenomenon in graph structures, which impedes the propagation of long-range information. Prior works have proposed a variety of graph rewiring concepts that aim at optimizing the spatial or spectral properties of graphs to promote the signal propagation. However, such approaches inevitably deteriorate the original graph topology, which may lead to a distortion of information flow. To address this, we introduce an expanded width-aware (PANDA) message passing, a new message passing paradigm where nodes with high centrality, a potential source of over-squashing, are selectively expanded in width to encapsulate the growing influx of signals from distant nodes. Experimental results show that our method outperforms existing rewiring methods, suggesting that selectively expanding the hidden state of nodes can be a compelling alternative to graph rewiring for addressing the over-squashing.
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable. We use a link-cut tree data structure and parallelism to lower the complexity of computing extended persistence, obtaining a speedup of more than 60x over the state-of-the-art for extended persistence computation. This makes extended persistence feasible for machine learning. We show that, under certain conditions, extended persistence surpasses both the WL[1] graph isomorphism test and 0-dimensional barcodes in terms of expressivity because it adds more global (topological) information. In particular, arbitrarily long cycles can be represented, which is difficult for finite receptive field message passing graph neural networks. Furthermore, we show the effectiveness of our method on real world datasets compared to many existing recent graph representation learning methods.
Message-passing graph neural networks (GNNs) excel at capturing local relationships but struggle with long-range dependencies in graphs. In contrast, graph transformers (GTs) enable global information exchange but often oversimplify the graph structure by representing graphs as sets of fixed-length vectors. This work introduces a novel architecture that overcomes the shortcomings of both approaches by combining the long-range information of random walks with local message passing. By treating random walks as sequences, our architecture leverages recent advances in sequence models to effectively capture long-range dependencies within these walks. Based on this concept, we propose a framework that offers (1) more expressive graph representations through random walk sequences, (2) the ability to utilize any sequence model for capturing long-range dependencies, and (3) the flexibility by integrating various GNN and GT architectures. Our experimental evaluations demonstrate that our approach achieves significant performance improvements on 19 graph and node benchmark datasets, notably outperforming existing methods by up to 13\% on the PascalVoc-SP and COCO-SP datasets. The code is available at https://github.com/BorgwardtLab/NeuralWalker.
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of shift equivariance, which is the basis of convolution networks on images, to general graphs. Unlike images, graphs do not have a natural notion of domain translation. Therefore, we consider the graph functional shifts as the symmetry group: the unitary operators that commute with the graph shift operator. Notably, such symmetries operate in the signal space rather than directly in the spatial space. We remark that each linear filter layer of a standard spectral graph neural network (GNN) commutes with graph functional shifts, but the activation function breaks this symmetry. Instead, we propose nonlinear spectral filters (NLSFs) that are fully equivariant to graph functional shifts and show that they have universal approximation properties. The proposed NLSFs are based on a new form of spectral domain that is transferable between graphs. We demonstrate the superior performance of NLSFs over existing spectral GNNs in node and graph classification benchmarks.
Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial optimization (CO) problems is much less explored. Here, we introduce GCON, a novel GNN architecture that leverages a complex filter bank and localized attention mechanisms to solve CO problems on graphs. We show how our method differentiates itself from prior GNN-based CO solvers and how it can be effectively applied to the maximum cut, minimum dominating set, and maximum clique problems in a unsupervised learning setting. GCON is competitive across all tasks and consistently outperforms other specialized GNN-based approaches, and is on par with the powerful Gurobi solver on the max-cut problem. We provide an open-source implementation of our work at https://github.com/WenkelF/copt.
Spatial Message Passing Graph Neural Networks (MPGNNs) are widely used for learning on graph-structured data. However, key limitations of l-step MPGNNs are that their "receptive field" is typically limited to the l-hop neighborhood of a node and that information exchange between distant nodes is limited by over-squashing. Motivated by these limitations, we propose Spatio-Spectral Graph Neural Networks (S$^2$GNNs) -- a new modeling paradigm for Graph Neural Networks (GNNs) that synergistically combines spatially and spectrally parametrized graph filters. Parameterizing filters partially in the frequency domain enables global yet efficient information propagation. We show that S$^2$GNNs vanquish over-squashing and yield strictly tighter approximation-theoretic error bounds than MPGNNs. Further, rethinking graph convolutions at a fundamental level unlocks new design spaces. For example, S$^2$GNNs allow for free positional encodings that make them strictly more expressive than the 1-Weisfeiler-Lehman (WL) test. Moreover, to obtain general-purpose S$^2$GNNs, we propose spectrally parametrized filters for directed graphs. S$^2$GNNs outperform spatial MPGNNs, graph transformers, and graph rewirings, e.g., on the peptide long-range benchmark tasks, and are competitive with state-of-the-art sequence modeling. On a 40 GB GPU, S$^2$GNNs scale to millions of nodes.
Graph Neural Networks (GNNs) are computationally demanding and inefficient when applied to graph classification tasks in resource-constrained edge scenarios due to their inherent process, involving multiple rounds of forward and backward propagation. As a lightweight alternative, Hyper-Dimensional Computing (HDC), which leverages high-dimensional vectors for data encoding and processing, offers a more efficient solution by addressing computational bottleneck. However, current HDC methods primarily focus on static graphs and neglect to effectively capture node attributes and structural information, which leads to poor accuracy. In this work, we propose CiliaGraph, an enhanced expressive yet ultra-lightweight HDC model for graph classification. This model introduces a novel node encoding strategy that preserves relative distance isomorphism for accurate node connection representation. In addition, node distances are utilized as edge weights for information aggregation, and the encoded node attributes and structural information are concatenated to obtain a comprehensive graph representation. Furthermore, we explore the relationship between orthogonality and dimensionality to reduce the dimensions, thereby further enhancing computational efficiency. Compared to the SOTA GNNs, extensive experiments show that CiliaGraph reduces memory usage and accelerates training speed by an average of 292 times(up to 2341 times) and 103 times(up to 313 times) respectively while maintaining comparable accuracy.
Graph Prompt Learning (GPL) bridges significant disparities between pretraining and downstream applications to alleviate the knowledge transfer bottleneck in real-world graph learning. While GPL offers superior effectiveness in graph knowledge transfer and computational efficiency, the security risks posed by backdoor poisoning effects embedded in pretrained models remain largely unexplored. Our study provides a comprehensive analysis of GPL's vulnerability to backdoor attacks. We introduce \textit{CrossBA}, the first cross-context backdoor attack against GPL, which manipulates only the pretraining phase without requiring knowledge of downstream applications. Our investigation reveals both theoretically and empirically that tuning trigger graphs, combined with prompt transformations, can seamlessly transfer the backdoor threat from pretrained encoders to downstream applications. Through extensive experiments involving 3 representative GPL methods across 5 distinct cross-context scenarios and 5 benchmark datasets of node and graph classification tasks, we demonstrate that \textit{CrossBA} consistently achieves high attack success rates while preserving the functionality of downstream applications over clean input. We also explore potential countermeasures against \textit{CrossBA} and conclude that current defenses are insufficient to mitigate \textit{CrossBA}. Our study highlights the persistent backdoor threats to GPL systems, raising trustworthiness concerns in the practices of GPL techniques.
In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries efficiently by averaging over input-dependent subsets of the group, i.e., frames. What we currently lack is a principled understanding of the design of frames. In this work, we introduce a canonicalization perspective that provides an essential and complete view of the design of frames. Canonicalization is a classic approach for attaining invariance by mapping inputs to their canonical forms. We show that there exists an inherent connection between frames and canonical forms. Leveraging this connection, we can efficiently compare the complexity of frames as well as determine the optimality of certain frames. Guided by this principle, we design novel frames for eigenvectors that are strictly superior to existing methods -- some are even optimal -- both theoretically and empirically. The reduction to the canonicalization perspective further uncovers equivalences between previous methods. These observations suggest that canonicalization provides a fundamental understanding of existing frame-averaging methods and unifies existing equivariant and invariant learning methods. Code is available at https://github.com/PKU-ML/canonicalization.
We present a novel end-to-end framework that generates highly compact (typically 6-15 dimensions), discrete (int4 type), and interpretable node representations, termed node identifiers (node IDs), to tackle inference challenges on large-scale graphs. By employing vector quantization, we compress continuous node embeddings from multiple layers of a Graph Neural Network (GNN) into discrete codes, applicable under both self-supervised and supervised learning paradigms. These node IDs capture high-level abstractions of graph data and offer interpretability that traditional GNN embeddings lack. Extensive experiments on 34 datasets, encompassing node classification, graph classification, link prediction, and attributed graph clustering tasks, demonstrate that the generated node IDs significantly enhance speed and memory efficiency while achieving competitive performance compared to current state-of-the-art methods.
Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.
Graph neural networks (GNNs) have achieved state-of-the-art performance in graph representation learning. Message passing neural networks, which learn representations through recursively aggregating information from each node and its neighbors, are among the most commonly-used GNNs. However, a wealth of structural information of individual nodes and full graphs is often ignored in such process, which restricts the expressive power of GNNs. Various graph data augmentation methods that enable the message passing with richer structure knowledge have been introduced as one main way to tackle this issue, but they are often focused on individual structure features and difficult to scale up with more structure features. In this work we propose a novel approach, namely collective structure knowledge-augmented graph neural network (CoS-GNN), in which a new message passing method is introduced to allow GNNs to harness a diverse set of node- and graph-level structure features, together with original node features/attributes, in augmented graphs. In doing so, our approach largely improves the structural knowledge modeling of GNNs in both node and graph levels, resulting in substantially improved graph representations. This is justified by extensive empirical results where CoS-GNN outperforms state-of-the-art models in various graph-level learning tasks, including graph classification, anomaly detection, and out-of-distribution generalization.
Graph Neural Networks (GNNs) are powerful tools for graph classification. One important operation for GNNs is the downsampling or pooling that can learn effective embeddings from the node representations. In this paper, we propose a new hierarchical pooling operation, namely the Edge-Node Attention-based Differentiable Pooling (ENADPool), for GNNs to learn effective graph representations. Unlike the classical hierarchical pooling operation that is based on the unclear node assignment and simply computes the averaged feature over the nodes of each cluster, the proposed ENADPool not only employs a hard clustering strategy to assign each node into an unique cluster, but also compress the node features as well as their edge connectivity strengths into the resulting hierarchical structure based on the attention mechanism after each pooling step. As a result, the proposed ENADPool simultaneously identifies the importance of different nodes within each separated cluster and edges between corresponding clusters, that significantly addresses the shortcomings of the uniform edge-node based structure information aggregation arising in the classical hierarchical pooling operation. Moreover, to mitigate the over-smoothing problem arising in existing GNNs, we propose a Multi-distance GNN (MD-GNN) model associated with the proposed ENADPool operation, allowing the nodes to actively and directly receive the feature information from neighbors at different random walk steps. Experiments demonstrate the effectiveness of the MD-GNN associated with the proposed ENADPool.
Diagnosing epilepsy requires accurate seizure detection and classification, but traditional manual EEG signal analysis is resource-intensive. Meanwhile, automated algorithms often overlook EEG's geometric and semantic properties critical for interpreting brain activity. This paper introduces NeuroGNN, a dynamic Graph Neural Network (GNN) framework that captures the dynamic interplay between the EEG electrode locations and the semantics of their corresponding brain regions. The specific brain region where an electrode is placed critically shapes the nature of captured EEG signals. Each brain region governs distinct cognitive functions, emotions, and sensory processing, influencing both the semantic and spatial relationships within the EEG data. Understanding and modeling these intricate brain relationships are essential for accurate and meaningful insights into brain activity. This is precisely where the proposed NeuroGNN framework excels by dynamically constructing a graph that encapsulates these evolving spatial, temporal, semantic, and taxonomic correlations to improve precision in seizure detection and classification. Our extensive experiments with real-world data demonstrate that NeuroGNN significantly outperforms existing state-of-the-art models.
We propose a new graph convolutional block, called MusGConv, specifically designed for the efficient processing of musical score data and motivated by general perceptual principles. It focuses on two fundamental dimensions of music, pitch and rhythm, and considers both relative and absolute representations of these components. We evaluate our approach on four different musical understanding problems: monophonic voice separation, harmonic analysis, cadence detection, and composer identification which, in abstract terms, translate to different graph learning problems, namely, node classification, link prediction, and graph classification. Our experiments demonstrate that MusGConv improves the performance on three of the aforementioned tasks while being conceptually very simple and efficient. We interpret this as evidence that it is beneficial to include perception-informed processing of fundamental musical concepts when developing graph network applications on musical score data.
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the solution. Graph kernels that implicitly capture the correlations among substructures in diverse graphs have exhibited great discriminative power in graph classification, so we pioneeringly investigate their potential in counting subgraph isomorphisms and further explore the augmentation of kernel capability through various variants, including polynomial and Gaussian kernels. Through comprehensive analysis, we enhance the graph kernels by incorporating neighborhood information. Finally, we present the results of extensive experiments to demonstrate the effectiveness of the enhanced graph kernels and discuss promising directions for future research.
One main challenge in imbalanced graph classification is to learn expressive representations of the graphs in under-represented (minority) classes. Existing generic imbalanced learning methods, such as oversampling and imbalanced learning loss functions, can be adopted for enabling graph representation learning models to cope with this challenge. However, these methods often directly operate on the graph representations, ignoring rich discriminative information within the graphs and their interactions. To tackle this issue, we introduce a novel multi-scale oversampling graph neural network (MOSGNN) that learns expressive minority graph representations based on intra- and inter-graph semantics resulting from oversampled graphs at multiple scales - subgraph, graph, and pairwise graphs. It achieves this by jointly optimizing subgraph-level, graph-level, and pairwise-graph learning tasks to learn the discriminative information embedded within and between the minority graphs. Extensive experiments on 16 imbalanced graph datasets show that MOSGNN i) significantly outperforms five state-of-the-art models, and ii) offers a generic framework, in which different advanced imbalanced learning loss functions can be easily plugged in and obtain significantly improved classification performance.