Contrast pyramids have shown excellent reconstructions for several images with only a few number of high contrasts. The contrast histogram of the image shows the distribution of contrasts and allows to select a bound that limits the mean reconstruction error. A total order of the vertices enables a both the ordering of the edges with the same contrast and, together with max-link strategy, generates efficiently the contraction kernels of the pyramid. A spiral total order pushes the surviving vertices geometrically towards the center of the image.
Graph Neural Networks (GNNs) have demonstrated strong capabilities in learning from structured data. Yet efficiently capturing cycle-related information remains a computational challenge. In this work, we introduce a novel GNN called Grammatical Path Network (GPN) to efficiently capture cycle-related information inside graph structures. GPN leverage Context-Free Grammars (CFGs) for cycle counting through path precomputation. Inspired by the Graph Substructure Network (GSN) framework and recent advances in GNN expressiveness, GPN exploits CFG-based representations to encode cycles of length l + 1 by precomputing paths of length l at the edge level. This formulation eliminates the need for explicit cycle counting, while maintaining strong predictive performance. Our experiments on benchmark datasets demonstrate that GPN achieves comparable or superior results to GSN in tasks requiring cycle-aware representations, highlighting its efficiency and effectiveness. These findings suggest that CFG-guided path precomputation offers a scalable alternative for capturing higher-order structural dependencies in graph-based learning.
Graph Convolutional Networks (GCNs) have recently gained significant attention due to the success of Convolutional Neural Networks in image and language processing, as well as the prevalence of data that can be represented as graphs. However, GCNs are limited by the size of the graphs they can handle and by the oversmoothing problem, which can be caused by the depth or the large receptive field of these networks. Existing approaches address these limitations by leveraging minibatch training paradigm. However, the strategy of selecting subgraphs to form minibatches is a challenging task because of the dependency between nodes. In this work, we propose a general framework for generating minibatches in an effective way that ensures minimal loss of node interdependence information, preserves the original graph properties, and diversifies the samples for the GCN to improve generalization. We test our training process on real-world datasets with several well-known GCN models and demonstrate the improved results compared to existing methods.
In this paper, we introduce a Generalized Biased Infinity Laplacian on graphs, which is an interpolation between two eikonal operators. Within this framework, we investigate evolution equations governed by this class of operators, establishing the existence and uniqueness of their solutions. Finally, we explore the application of these operators to general functions for solving various problems in machine learning.
Document entity recognition is a critical task in the field of document analysis. While many large language models have demonstrated success in this domain, they often fail to incorporate the spatial layout relationships between entities within a document. In this work, we introduce VisHubGAT, a novel graph-based model that integrates visible connectivity and hub nodes to enhance entity classification. Our approach constructs a document graph representation where hub nodes aggregate label-specific features, leveraging pre-trained models such as BERT and LayoutLMv3. Additionally, we introduce multi-type edges to encode both spatial and semantic relationships, and a Graph Attention Network (GAT) with edge-aware attention, which incorporates edge features into the attention mechanism for improved relational modeling. An edge classification layer further refines entity connectivity. Our approach effectively captures inter-entity relationships within the document, thereby enhancing the entity classification capabilities of large language models on public datasets (FUNSD, CORD, DocILE), showing state-of-the-art results by using different modalities. Ablation studies highlight the importance of our structured graph design for document entity recognition.
The proliferation of online code repositories, such as GitHub and GitLab, has increased security risks related to the spread of malware through source code, including compromised libraries and obfuscated code. Traditional detection methods, such as static and dynamic analysis, have shown limitations when faced with advanced threats. To address this issue, we propose an approach based on Graph Neural Networks (GNN) to enhance malware detection in code repositories. Graphs provide an effective way to model the complex relationships within a program, such as interactions between functions, classes, modules, and external dependencies. This is particularly useful for identifying specific patterns of complex malicious behavior. Our model detects anomalies by analyzing the program internal interactions in addition to the exact code content. Our method extracts call graphs and metadata (such as descriptions and README files) from code repositories. The metadata is converted into vectors using a natural language embedding model, then merged with the embeddings of call graphs generated by GNNs. This combined representation is used by a supervised classifier to detect malicious repositories. The results show strong performance in precision, recall, and F1-score, validating the effectiveness of our approach.
In order to monitor climate change in Switzerland, the Federal Office for the Environment has been measuring river water temperature at 81 water stations for over 40 years. Based on these measurements and the underlying river network, we create a novel graph regression problem with a total of 3,480 graphs. The task is to predict the water temperature of output nodes by using a subset of input nodes. Depending on the subset, this creates challenging information bottlenecks and long-range dependencies. In a first contribution, we set RMSE baselines for four standard Graph Neural Networks (GNNs). Namely, we employ and compare GCN, GIN, GAT, and GraphSAGE architectures with up to 7 layers. In a second contribution, we analyze how noise propagates through such networks. In our evaluation, we observe that the GNN models degenerate more severely than alternative architectures. This empirical result shows that the message passing framework can harm models in presence of noise, a rarely mentioned limitation we would like to address in future research.
This study explores the use of Graph Neural Networks (GNNs) for image semantic segmentation, focusing on super-pixel-based approaches to ensure reasonable use of computational power. We evaluate various GNN modules on synthetic datasets of varying complexity, using a hierarchical GNN architecture inspired by U-Net. Our results show that GNNs with attention mechanisms perform well in handling noisy data and reconstructing complex shapes, sometimes surpassing traditional Convolutional Neural Networks (CNNs). Future research will assess the efficacy of this approach on real-world datasets.
Graph representations have emerged as a powerful tool in medical imaging to analyze complex structures such as the brain. In particular, studying the geometry of the brain surface provides valuable insights into individual characteristics. To model the brain as a graph, sulcal graphs are derived from MRI data by assigning a node to each fold of the cortical surface and connecting these nodes based on their adjacency. This approach encodes the geometry of the brain surface, making sulcal graphs a relevant data representation for predictive models. In this study, we explore the effectiveness of Graph Neural Networks (GNNs) to extract meaningful information from these graph representations, using sex classification as a pretext task. Our experiments reveal that the structural information captured by the graph is largely driven by the 3D coordinates of the nodes, raising questions about the added value of graph connectivity in these representations. Additionally, we find that conventional Multi-Layer Perceptron (MLP) models achieve comparable or superior performance to GNNs, suggesting that graph structure may not provide significant additional discriminative power in this specific task. These findings highlight the challenges of defining optimal GNN architectures for sulcal graphs and motivate further investigations into alternative representations and learning paradigms.
Due to their intrinsic capabilities in capturing, modeling, and representing relationships between pieces of information, graphs have been used in a wide variety of application domains. Surprisingly, over the past two decades, graphs in general-and graph-based algorithms in particular-have been employed for a challenging computer vision task: saliency detection. More specifically, researchers have explored ways to model saliency in images using graph structures, graph manifolds, and neural networks to identify the most significant and attention-grabbing regions and objects in a visual scene. From another perspective, saliency in the context of graphs refers to nodes and edges (i.e., subgraphs) that hold greater importance, such as those exhibiting stronger connectivity or structural significance. This early study explores underexamined topics and introduces a novel link between node saliency in graphs and salient objects in images. Promising results suggest the potential to inspire new research on using graphs in computer vision and pattern recognition.
Graph Neural Networks (GNNs) have excelled across various domains, but recent studies show they are vulnerable to adversarial attacks. Among these, Node Injection Attacks (NIA) are a practical method, injecting malicious nodes to disrupt the model's performance. In this paper, we focus on a more practical NIA scenario, where the attacker can only inject a small number of nodes to degrade the global performance of GNNs, and no information beyond the input features and adjacency relations is available to the attacker. We establish the relationship between resistance distance and graph connectivity and use it to guide the connections between injected and original nodes. To enhance attack effectiveness while reducing detectability, we replicate distant features from the original graph as the initial features of the injected nodes. Furthermore, the adjacency and feature matrices of the injected nodes are optimized in an unsupervised manner using contrastive learning. Based on these ideas, we propose the Resistance Distance Guided Node Injection Attack (RDGNIA). Experiments on three benchmark datasets demonstrate the superiority of our method compared to state-of-the-art approaches.
A key challenge in structural pattern recognition is quantifying the dissimilarity or similarity between graphs. Traditional methods that solve this challenge, such as the graph edit distance, assign costs to structural differences of the graphs to measure their dissimilarity. More recent approaches leverage graph kernels or graph neural networks for the same task. In the present paper, we propose a novel framework for graph dissimilarity computation that consists of three major steps. Using GNNs, we first embed graphs into real vector spaces. Then, in a second step, we construct convex hulls from these embeddings. In the third step, we extract geometric features from these hulls, from which we finally derive dissimilarity values between the graphs. The experimental evaluation on a few data sets demonstrates that our novel approach achieves comparable classification performance to that of reference systems. At the same time, we observe substantial reductions of the computation time.
Graph anomaly detection (GAD) is a fundamental task in numerous real-world applications, including fraud detection, network security, and financial risk assessment. However, existing approaches struggle with label scarcity, limiting the effectiveness of purely supervised and semi-supervised models. Co-training frameworks have demonstrated improvements through collaborative learning, but they remain constrained by their rigid structure and reliance on graph-specific architectures. In this paper, we introduce TExGAD, a novel collaborative learning framework that extends co-training by introducing a modular triple-exchange mechanism that leverages three detectors: (1) a flexible Semisupervised Detector, allowing for the integration of both shallow and nongraph-specific models, (2) an Unsupervised Detector that identifies structural deviations in the graph without relying on labeled data, making it particularly effective at detecting normal nodes and scattered anomalies, and (3) a Deep Detector that captures richer anomaly representations by leveraging high-confidence predictions from the other detectors. Furthermore, TExGAD integrates a set of specialized loss functions, ensuring a balance between diversity, alignment, and independent learning and an adaptive scoring function that further refines anomaly detection by dynamically weighting detector contributions based on their confidence. Our experiments demonstrate the effectiveness of TExGAD in low-label environments, highlighting its adaptability and robustness.
Financial organisations often struggle to effectively leverage the information contained within transactional networks observed in their data. This is because most transactional networks are massive and are highly dynamic, evolving constantly over time. Existing graph-based representation learning approaches studied in financial literature struggle to adapt to these unique challenges. We demonstrate the application of GraphSAGE, an inductive representation learning algortihm, to a real-world transactional network and showcase how to effectively utilise this information-rich asset in the context of banking. We show how the inductive capabilties of GraphSAGE enable inference over unseen nodes, making it particularly useful for embedding dynamic networks. We overcome scalability challenges faced by other approaches by implementing a GPU-enabled sampling-based training algorithm. This paper also shares outcomes from exploratory analysis on the resulting embeddings revealing interpretable clusters aligned with customer attributes. Finally, we illustrate how the embeddings can be utilised in downstream classification tasks by using them in a money mule detection model, demonstrating that the embeddings help improve the prioritisation of high-risk accounts. This work serves as a blueprint for financial organisations to practically harness graph-based representation learning to gain actionable insights from their transactional networks.
Graph clustering is a fundamental task in network analysis, with applications ranging from community detection to protein complex identification. While Graph Neural Networks (GNNs) have shown promising results in this domain, they often struggle to balance local structure preservation with global cluster separation. We present a novel information-theoretic framework that enhances graph clustering through differentiable Rényi entropy optimization. Our approach introduces a computationally efficient masked entropy loss that encourages informative node representations while respecting graph topology. By integrating this framework with state-of-the-art GNN architectures, we achieve significant improvements in clustering quality across multiple benchmark datasets.
Graph Neural Networks (GNNs) have advanced key information extraction (KIE) in document AI, but existing methods remain monolingual. We introduce Doc2Graph-X, a multilingual extension of Doc2Graph, leveraging word-level and sentence-level embeddings for robust cross-lingual document representation. Our framework constructs graph-based structures where a node classifier performs semantic entity recognition (SER) and an edge classifier handles relation extraction (RE) to predict links between entities. Evaluated on the XFUND dataset across seven languages, Doc2Graph-X outperforms existing baselines, demonstrating strong multilingual adaptability. Additional results on FUNSD validate its effectiveness in monolingual settings. Our approach enables structured multilingual document understanding while preserving task-agnostic adaptability. The code (https://github.com/ biswassanket/doc2graph multi.git) will be made available upon acceptance.
Accurately predicting subject status from brain network data is a complex task that requires advanced machine learning techniques. In this work, we propose a comprehensive methodology and pipeline for applying supervised graph learning models, specifically Graph Neural Networks, to this task using brain network information derived from diffusion tensor imaging, gray matter and resting-state functional MRI adjacency matrices. Our approach includes a graph pruning step to retain the most relevant edges while preserving crucial information, the generation of node features to enhance graph representations, the creation of synthetic data to balance the dataset and improve training, and the design and training of GNN models for both multi-class and binary classification tasks. Experimental results in a cohort of people with multiple sclerosis and healthy volunteers demonstrate that our methodology effectively captures meaningful patterns in brain graphs, leading to improved classification performance.
Deep learning has been extremely successful in a wide range of tasks in domains as diverse as image classification and natural language processing. However, at the same time, learning models may fail spectacularly, a phenomenon sometimes attributed to learning spurious correlations, or shortcuts, that deviate from the desired decision rule. In this paper, we perform an experimental analysis of the shortcut learning phenomenon on graphs, exposing the critical role played by the inductive bias of the learning model. Our results pave the way for a future principled theoretical analysis of this relevant phenomenon.
The discipline of graph-based machine learning, which focuses on learning from structured graph data, is expanding rapidly. Numerous applications in recommendation systems, bioinformatics, and social network analysis fall within this domain. However, traditional Graph Neural Networks (GNNs) face difficulties when dealing with datasets that frequently contain structured and graph data. Our approach addresses this challenge by creating a proposed fusion model of GNN and Gradient Boosting Decision Trees (GBDTs). We investigated the effectiveness of using the GNN and GBDT based fusion model using logistic regression by combining the embeddings of GNN and GBDT, stacking the predictions from GBDT variants for node classification and graph classification. The generality of the model is tested and validated on one heterogeneous and two homogeneous state-of-the-art datasets with average accuracy of A: Freebase: 0.6875, B: Letters (Low: 96.62, Med: 84.81, High: 78.06), C:Fingerprints:80.45, D:OGBGMolHIV:89.10 outperforming individual methods. The results indicated that the fusion approach was effective in accurately classifying complete graphs and nodes, although their performance varied depending on the dataset and the characteristics of the graph being analyzed. This shows that the applied technique can get the appropriate results. The supplementary material of our work is publicly available at (https://github. com/mr49online/fusion_model).
Subgraph isomorphism is a challenging problem involving the search for structural patterns in graphs. It has numerous applications across various fields, and many specialized algorithms have been proposed. However, existing sequential algorithms struggle with extremely large and sparse graphs, particularly when the pattern size is very small with respect to the target graph. Recently, GPU-based approaches have been introduced to address this issue; but, while they are highly effective at exploiting GPU parallelism, these methods are also memory-intensive. In this paper, we present VF-GPU, a novel hybrid algorithm that leverages both CPU and GPU architectures to efficiently solve the subgraph isomorphism problem. Our approach is based on a state space representation (SSR) and employs a limited breadth-first search (BFS) strategy to constrain state generation during exploration. This enables efficient parallelism while controlling memory usage. We evaluated VF-GPU against VF3, VF3-L, and the GPU-based GSI algorithm. The experiments, conducted on a large sparse graph with over 300,000 nodes, demonstrate the effectiveness of our method across different query sizes and label distributions.
