Topology-Aware PAC-Bayesian Generalization Analysis for Graph Neural Networks

• URL: http://arxiv.org/abs/2604.10553v1
• Date: Sun, 12 Apr 2026 09:52:27 GMT
• Title: Topology-Aware PAC-Bayesian Generalization Analysis for Graph Neural Networks
• Abstract summary: We propose a topology-aware PAC-Bayesian norm-based generalization framework for graph convolutional networks (GCNs)<n>By imposing different structures on sensitivity matrices from both spatial and spectral perspectives, we derive a family of generalization error bounds with graph structures embedded.<n> Notably, the proposed framework explicitly integrates graph structural properties into the generalization analysis, enabling a unified inspection of GNN generalization behavior.
• Score: 21.139538521229273
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph neural networks have demonstrated excellent applicability to a wide range of domains, including social networks, biological systems, recommendation systems, and wireless communications. Yet a principled theoretical understanding of their generalization behavior remains limited, particularly for graph classification tasks where complex interactions between model parameters and graph structure play a crucial role. Among existing theoretical tools, PAC-Bayesian norm-based generalization bounds provide a flexible and data-dependent framework; however, current results for GNNs often restrict the exploitation of graph structures. In this work, we propose a topology-aware PAC-Bayesian norm-based generalization framework for graph convolutional networks (GCNs) that extends a previously developed framework to graph-structured models. Our approach reformulates the derivation of generalization bounds as a stochastic optimization problem and introduces sensitivity matrices that measure the response of classification outputs with respect to structured weight perturbations. By imposing different structures on sensitivity matrices from both spatial and spectral perspectives, we derive a family of generalization error bounds with graph structures explicitly embedded. Such bounds could recover existing results as special cases, while yielding bounds that are tighter than state-of-the-art PAC-Bayesian bounds for GNNs. Notably, the proposed framework explicitly integrates graph structural properties into the generalization analysis, enabling a unified inspection of GNN generalization behavior from both spatial aggregation and spectral filtering viewpoints.

Related papers

• PAC-Bayesian Adversarially Robust Generalization for Message Passing Graph Neural Networks: A Sensitivity Analysis [80.64607823130437]
  We extend PAC-Bayesian framework from deep neural networks to message passing GNNs.<n>We derive a tighter robust generalization bound in the adversarial setting.
  arXiv  Detail & Related papers  (2026-06-04T15:31:21Z)
• Rethinking Generalization in Graph Neural Networks: A Structural Complexity Perspective [41.727617218821386]
  Graph neural networks (GNNs) have emerged as a fundamental tool for learning from graph-structured data.<n>We ask: does the graph structure actually influence generalization, and if so, by how much?<n>To answer the first question and validate our intuition, we theoretically prove that incorporating more edges into the prediction process transforms the input representations to be overly accommodating to the output model, thereby inducing overfitting.<n>To address the second question, we formulate a structural complexity measure based on the number of effective edges and derive a Rademacher complexity-based generalization bound.
  arXiv  Detail & Related papers  (2026-05-13T14:32:46Z)
• Towards A Unified PAC-Bayesian Framework for Norm-based Generalization Bounds [63.47271262149291]
  We propose a unified framework for PAC-Bayesian norm-based generalization.<n>The key to our approach is a sensitivity matrix that quantifies the network outputs with respect to structured weight perturbations.<n>We derive a family of generalization bounds that recover several existing PAC-Bayesian results as special cases.
  arXiv  Detail & Related papers  (2026-01-13T00:42:22Z)
• On the Impact of Graph Neural Networks in Recommender Systems: A Topological Perspective [49.391877616394765]
  In recommender systems, user-item interactions can be modeled as a bipartite graph, where user and item nodes are connected by undirected edges.<n>This graph-based view has motivated the rapid adoption of graph neural networks (GNNs)<n>Despite their empirical success, the reasons why GNNs offer systematic advantages over other approaches remain only partially understood.
  arXiv  Detail & Related papers  (2025-12-08T10:19:43Z)
• PAC-Bayesian Generalization Bounds for Graph Convolutional Networks on Inductive Node Classification [20.5924958759845]
  We present a PAC-Bayesian theoretical analysis of graph convolutional networks (GCNs) for inductive node classification.<n>We derive novel generalization bounds for one-layer GCNs that explicitly incorporate the effects of data dependency and non-stationarity.<n>We extend our analysis to two-layer GCNs, and reveal that it requires stronger assumptions on graph topology to guarantee convergence.
  arXiv  Detail & Related papers  (2025-09-08T12:10:54Z)
• A Manifold Perspective on the Statistical Generalization of Graph Neural Networks [84.01980526069075]
  We take a manifold perspective to establish the statistical generalization theory of GNNs on graphs sampled from a manifold in the spectral domain.<n>We prove that the generalization bounds of GNNs decrease linearly with the size of the graphs in the logarithmic scale, and increase linearly with the spectral continuity constants of the filter functions.
  arXiv  Detail & Related papers  (2024-06-07T19:25:02Z)
• Generalization of Graph Neural Networks through the Lens of Homomorphism [7.223313563198697]
  We propose to study the generalization of Graph Neural Networks (GNNs) through a novel perspective - analyzing the entropy of graph homomorphism. By linking graph homomorphism with information-theoretic measures, we derive generalization bounds for both graph and node classifications. These bounds are capable of capturing subtleties inherent in various graph structures, including but not limited to paths, cycles and cliques.
  arXiv  Detail & Related papers  (2024-03-10T03:51:59Z)
• On the Topology Awareness and Generalization Performance of Graph Neural Networks [6.598758004828656]
  We introduce a comprehensive framework to characterize the topology awareness of GNNs across any topological feature. We conduct a case study using the intrinsic graph metric the shortest path distance on various benchmark datasets.
  arXiv  Detail & Related papers  (2024-03-07T13:33:30Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• A PAC-Bayesian Approach to Generalization Bounds for Graph Neural Networks [99.46182575751271]
  We derive generalization bounds for the two primary classes of graph neural networks (GNNs) Our result reveals that the maximum node degree and spectral norm of the weights govern the generalization bounds of both models.
  arXiv  Detail & Related papers  (2020-12-14T16:41:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.