Graph-based learning provides a powerful framework for modeling complex relational structures; however, its application within the domain of wireless security remains significantly underexplored. In this work, we introduce the first application of graph-based learning for jamming source localization, addressing the imminent threat of jamming attacks in wireless networks. Unlike geometric optimization techniques that struggle under environmental uncertainties and dense interference, we reformulate the localization as an inductive graph regression task. Our approach integrates structured node representations that encode local and global signal aggregation, ensuring spatial coherence and adaptive signal fusion. To enhance robustness, we incorporate an attention-based \ac{GNN} that adaptively refines neighborhood influence and introduces a confidence-guided estimation mechanism that dynamically balances learned predictions with domain-informed priors. We evaluate our approach under complex \ac{RF} environments with various sampling densities, network topologies, jammer characteristics, and signal propagation conditions, conducting comprehensive ablation studies on graph construction, feature selection, and pooling strategies. Results demonstrate that our novel graph-based learning framework significantly outperforms established localization baselines, particularly in challenging scenarios with sparse and obfuscated signal information. Our code is available at https://github.com/tiiuae/gnn-jamming-source-localization.
Graph-level regression underpins many real-world applications, yet public benchmarks remain heavily skewed toward molecular graphs and citation networks. This limited diversity hinders progress on models that must generalize across both homogeneous and heterogeneous graph structures. We introduce RelSC, a new graph-regression dataset built from program graphs that combine syntactic and semantic information extracted from source code. Each graph is labelled with the execution-time cost of the corresponding program, providing a continuous target variable that differs markedly from those found in existing benchmarks. RelSC is released in two complementary variants. RelSC-H supplies rich node features under a single (homogeneous) edge type, while RelSC-M preserves the original multi-relational structure, connecting nodes through multiple edge types that encode distinct semantic relationships. Together, these variants let researchers probe how representation choice influences model behaviour. We evaluate a diverse set of graph neural network architectures on both variants of RelSC. The results reveal consistent performance differences between the homogeneous and multi-relational settings, emphasising the importance of structural representation. These findings demonstrate RelSC's value as a challenging and versatile benchmark for advancing graph regression methods.
Message-Passing Neural Networks (MPNNs) have become a cornerstone for processing and analyzing graph-structured data. However, their effectiveness is often hindered by phenomena such as over-squashing, where long-range dependencies or interactions are inadequately captured and expressed in the MPNN output. This limitation mirrors the challenges of the Effective Receptive Field (ERF) in Convolutional Neural Networks (CNNs), where the theoretical receptive field is underutilized in practice. In this work, we show and theoretically explain the limited ERF problem in MPNNs. Furthermore, inspired by recent advances in ERF augmentation for CNNs, we propose an Interleaved Multiscale Message-Passing Neural Networks (IM-MPNN) architecture to address these problems in MPNNs. Our method incorporates a hierarchical coarsening of the graph, enabling message-passing across multiscale representations and facilitating long-range interactions without excessive depth or parameterization. Through extensive evaluations on benchmarks such as the Long-Range Graph Benchmark (LRGB), we demonstrate substantial improvements over baseline MPNNs in capturing long-range dependencies while maintaining computational efficiency.
Point signatures based on the Laplacian operators on graphs, point clouds, and manifolds have become popular tools in machine learning for graphs, clustering, and shape analysis. In this work, we propose a novel point signature, the power spectrum signature, a measure on $\mathbb{R}$ defined as the squared graph Fourier transform of a graph signal. Unlike eigenvectors of the Laplacian from which it is derived, the power spectrum signature is invariant under graph automorphisms. We show that the power spectrum signature is stable under perturbations of the input graph with respect to the Wasserstein metric. We focus on the signature applied to classes of indicator functions, and its applications to generating descriptive features for vertices of graphs. To demonstrate the practical value of our signature, we showcase several applications in characterizing geometry and symmetries in point cloud data, and graph regression problems.
Positional encodings (PEs) are essential for effective graph representation learning because they provide position awareness in inherently position-agnostic transformer architectures and increase the expressive capacity of Graph Neural Networks (GNNs). However, designing powerful and efficient PEs for graphs poses significant challenges due to the absence of canonical node ordering and the scale of the graph. In this work, we identify four key properties that graph PEs should satisfy: stability, expressive power, scalability, and genericness. We find that existing eigenvector-based PE methods often fall short of jointly satisfying these criteria. To address this gap, we introduce PEARL, a novel framework of learnable PEs for graphs. Our primary insight is that message-passing GNNs function as nonlinear mappings of eigenvectors, enabling the design of GNN architectures for generating powerful and efficient PEs. A crucial challenge lies in initializing node features in a manner that is both expressive and permutation equivariant. We tackle this by initializing GNNs with random node inputs or standard basis vectors, thereby unlocking the expressive power of message-passing operations, while employing statistical pooling functions to maintain permutation equivariance. Our analysis demonstrates that PEARL approximates equivariant functions of eigenvectors with linear complexity, while rigorously establishing its stability and high expressive power. Experimental evaluations show that PEARL outperforms lightweight versions of eigenvector-based PEs and achieves comparable performance to full eigenvector-based PEs, but with one or two orders of magnitude lower complexity.
Message-passing Graph Neural Networks (GNNs) are often criticized for their limited expressiveness, issues like over-smoothing and over-squashing, and challenges in capturing long-range dependencies, while Graph Transformers (GTs) are considered superior due to their global attention mechanisms. Literature frequently suggests that GTs outperform GNNs, particularly in graph-level tasks such as graph classification and regression. In this study, we explore the untapped potential of GNNs through an enhanced framework, GNN+, which integrates six widely used techniques: edge feature integration, normalization, dropout, residual connections, feed-forward networks, and positional encoding, to effectively tackle graph-level tasks. We conduct a systematic evaluation of three classic GNNs, namely GCN, GIN, and GatedGCN, enhanced by the GNN+ framework across 14 well-known graph-level datasets. Our results show that, contrary to the prevailing belief, classic GNNs excel in graph-level tasks, securing top three rankings across all datasets and achieving first place in eight, while also demonstrating greater efficiency than GTs. This highlights the potential of simple GNN architectures, challenging the belief that complex mechanisms in GTs are essential for superior graph-level performance.
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.
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.
In the field of deep learning, Graph Neural Networks (GNNs) and Graph Transformer models, with their outstanding performance and flexible architectural designs, have become leading technologies for processing structured data, especially graph data. Traditional GNNs often face challenges in capturing information from distant vertices effectively. In contrast, Graph Transformer models are particularly adept at managing long-distance node relationships. Despite these advantages, Graph Transformer models still encounter issues with computational and storage efficiency when scaled to large graph datasets. To address these challenges, we propose an innovative Graph Neural Network (GNN) architecture that integrates a Top-m attention mechanism aggregation component and a neighborhood aggregation component, effectively enhancing the model's ability to aggregate relevant information from both local and extended neighborhoods at each layer. This method not only improves computational efficiency but also enriches the node features, facilitating a deeper analysis of complex graph structures. Additionally, to assess the effectiveness of our proposed model, we have applied it to citation sentiment prediction, a novel task previously unexplored in the GNN field. Accordingly, we constructed a dedicated citation network, ArXivNet. In this dataset, we specifically annotated the sentiment polarity of the citations (positive, neutral, negative) to enable in-depth sentiment analysis. Our approach has shown superior performance across a variety of tasks including vertex classification, link prediction, sentiment prediction, graph regression, and visualization. It outperforms existing methods in terms of effectiveness, as demonstrated by experimental results on multiple datasets.
Multi-relational networks capture intricate relationships in data and have diverse applications across fields such as biomedical, financial, and social sciences. As networks derived from increasingly large datasets become more common, identifying efficient methods for representing and analyzing them becomes crucial. This work extends the Prime Adjacency Matrices (PAMs) framework, which employs prime numbers to represent distinct relations within a network uniquely. This enables a compact representation of a complete multi-relational graph using a single adjacency matrix, which, in turn, facilitates quick computation of multi-hop adjacency matrices. In this work, we enhance the framework by introducing a lossless algorithm for calculating the multi-hop matrices and propose the Bag of Paths (BoP) representation, a versatile feature extraction methodology for various graph analytics tasks, at the node, edge, and graph level. We demonstrate the efficiency of the framework across various tasks and datasets, showing that simple BoP-based models perform comparably to or better than commonly used neural models while offering improved speed and interpretability.
Node regression consists in predicting the value of a graph label at a node, given observations at the other nodes. To gain some insight into the performance of various estimators for this task, we perform a theoretical study in a context where the graph is random. Specifically, we assume that the graph is generated by a Latent Position Model, where each node of the graph has a latent position, and the probability that two nodes are connected depend on the distance between the latent positions of the two nodes. In this context, we begin by studying the simplest possible estimator for graph regression, which consists in averaging the value of the label at all neighboring nodes. We show that in Latent Position Models this estimator tends to a Nadaraya Watson estimator in the latent space, and that its rate of convergence is in fact the same. One issue with this standard estimator is that it averages over a region consisting of all neighbors of a node, and that depending on the graph model this may be too much or too little. An alternative consists in first estimating the true distances between the latent positions, then injecting these estimated distances into a classical Nadaraya Watson estimator. This enables averaging in regions either smaller or larger than the typical graph neighborhood. We show that this method can achieve standard nonparametric rates in certain instances even when the graph neighborhood is too large or too small.
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.
Deep neural networks (DNNs) have demonstrated remarkable performance across various domains, yet their application to temporal graph regression tasks faces significant challenges regarding interpretability. This critical issue, rooted in the inherent complexity of both DNNs and underlying spatio-temporal patterns in the graph, calls for innovative solutions. While interpretability concerns in Graph Neural Networks (GNNs) mirror those of DNNs, to the best of our knowledge, no notable work has addressed the interpretability of temporal GNNs using a combination of Information Bottleneck (IB) principles and prototype-based methods. Our research introduces a novel approach that uniquely integrates these techniques to enhance the interpretability of temporal graph regression models. The key contributions of our work are threefold: We introduce the \underline{G}raph \underline{IN}terpretability in \underline{T}emporal \underline{R}egression task using \underline{I}nformation bottleneck and \underline{P}rototype (GINTRIP) framework, the first combined application of IB and prototype-based methods for interpretable temporal graph tasks. We derive a novel theoretical bound on mutual information (MI), extending the applicability of IB principles to graph regression tasks. We incorporate an unsupervised auxiliary classification head, fostering multi-task learning and diverse concept representation, which enhances the model bottleneck's interpretability. Our model is evaluated on real-world traffic datasets, outperforming existing methods in both forecasting accuracy and interpretability-related metrics.
HyperAggregation is a hypernetwork-based aggregation function for Graph Neural Networks. It uses a hypernetwork to dynamically generate weights in the size of the current neighborhood, which are then used to aggregate this neighborhood. This aggregation with the generated weights is done like an MLP-Mixer channel mixing over variable-sized vertex neighborhoods. We demonstrate HyperAggregation in two models, GraphHyperMixer is a model based on MLP-Mixer while GraphHyperConv is derived from a GCN but with a hypernetwork-based aggregation function. We perform experiments on diverse benchmark datasets for the vertex classification, graph classification, and graph regression tasks. The results show that HyperAggregation can be effectively used for homophilic and heterophilic datasets in both inductive and transductive settings. GraphHyperConv performs better than GraphHyperMixer and is especially strong in the transductive setting. On the heterophilic dataset Roman-Empire it reaches a new state of the art. On the graph-level tasks our models perform in line with similarly sized models. Ablation studies investigate the robustness against various hyperparameter choices. The implementation of HyperAggregation as well code to reproduce all experiments is available under https://github.com/Foisunt/HyperAggregation .
In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of a sequence of neighborhood aggregation (a.k.a., message-passing) layers, within which the representation of each node is updated based on those of its neighbors. The most expressive message-passing GNNs can be obtained through the use of the sum aggregator and of MLPs for feature transformation, thanks to their universal approximation capabilities. However, the limitations of MLPs recently motivated the introduction of another family of universal approximators, called Kolmogorov-Arnold Networks (KANs) which rely on a different representation theorem. In this work, we compare the performance of KANs against that of MLPs on graph learning tasks. We evaluate two different implementations of KANs using two distinct base families of functions, namely B-splines and radial basis functions. We perform extensive experiments on node classification, graph classification and graph regression datasets. Our results indicate that KANs are on-par with or better than MLPs on all studied tasks, making them viable alternatives, at the cost of some computational complexity. Code is available at https: //github.com/RomanBresson/KAGNN.
Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.
Graph pooling has gained attention for its ability to obtain effective node and graph representations for various downstream tasks. Despite the recent surge in graph pooling approaches, there is a lack of standardized experimental settings and fair benchmarks to evaluate their performance. To address this issue, we have constructed a comprehensive benchmark that includes 17 graph pooling methods and 28 different graph datasets. This benchmark systematically assesses the performance of graph pooling methods in three dimensions, i.e., effectiveness, robustness, and generalizability. We first evaluate the performance of these graph pooling approaches across different tasks including graph classification, graph regression and node classification. Then, we investigate their performance under potential noise attacks and out-of-distribution shifts in real-world scenarios. We also involve detailed efficiency analysis, backbone analysis, parameter analysis and visualization to provide more evidence. Extensive experiments validate the strong capability and applicability of graph pooling approaches in various scenarios, which can provide valuable insights and guidance for deep geometric learning research. The source code of our benchmark is available at https://github.com/goose315/Graph_Pooling_Benchmark.
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.
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.