Different Statistical Perspectives for Understanding Generalisation in Graph Neural Networks

• URL: http://arxiv.org/abs/2605.25452v1
• Date: Mon, 25 May 2026 06:02:31 GMT
• Title: Different Statistical Perspectives for Understanding Generalisation in Graph Neural Networks
• Abstract summary: Graph Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data.<n>We discuss the various perspectives used to study statistical generalisation in GNNs.
• Score: 9.227034835080307
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited mathematical understanding of the performance of GNNs. We discuss the various perspectives used to study statistical generalisation in GNNs. We identify three broad frameworks. The first approach, rooted in learning theory, relies on uniform convergence bounds and the complexity of the hypothesis class of specific GNN architectures. This approach also builds on the expressivity of GNNs, typically studied through the lens of graph isomorphism tests. The second principle is to simplify the neural architecture by analysing GNNs under the asymptotics of infinitely many parameters or infinite graph size. This approach approximates GNNs using Gaussian processes, neural tangent kernels or graphon neural network operators, which allow studying the generalisation or stability of trained GNNs. The third framework studies GNNs under random graph models, often the contextual stochastic block model, and derives non-asymptotic error rates using tools from high-dimensional statistics. We highlight some key theoretical results and discuss a few limitations and open research questions for each perspective.

Related papers

• On the Computational Capability of Graph Neural Networks: A Circuit Complexity Bound Perspective [28.497567290882355]
  Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data.<n>This paper explores the computational limitations of GNNs through the lens of circuit complexity.<n>Specifically, we analyze the circuit complexity of common GNN architectures and prove that under constraints of constant-depth layers, linear or sublinear embedding sizes, and precision, GNNs cannot solve key problems such as graph connectivity and graph isomorphism.
  arXiv  Detail & Related papers  (2025-01-11T05:54:10Z)
• Do graph neural network states contain graph properties? [5.222978725954348]
  We present a model explainability pipeline for Graph neural networks (GNNs) employing diagnostic classifiers.<n>This pipeline aims to probe and interpret the learned representations in GNNs across various architectures and datasets.
  arXiv  Detail & Related papers  (2024-11-04T15:26:07Z)
• 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)
• DEGREE: Decomposition Based Explanation For Graph Neural Networks [55.38873296761104]
  We propose DEGREE to provide a faithful explanation for GNN predictions. By decomposing the information generation and aggregation mechanism of GNNs, DEGREE allows tracking the contributions of specific components of the input graph to the final prediction. We also design a subgraph level interpretation algorithm to reveal complex interactions between graph nodes that are overlooked by previous methods.
  arXiv  Detail & Related papers  (2023-05-22T10:29:52Z)
• Learning Graph Neural Networks with Approximate Gradient Descent [24.49427608361397]
  Two types of graph neural networks (GNNs) are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs.
  arXiv  Detail & Related papers  (2020-12-07T02:54:48Z)
• A Unified View on Graph Neural Networks as Graph Signal Denoising [49.980783124401555]
  Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models can be regarded as solving a graph denoising problem. We instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes.
  arXiv  Detail & Related papers  (2020-10-05T04:57:18Z)
• The Surprising Power of Graph Neural Networks with Random Node Initialization [54.4101931234922]
  Graph neural networks (GNNs) are effective models for representation learning on relational data. Standard GNNs are limited in their expressive power, as they cannot distinguish beyond the capability of the Weisfeiler-Leman graph isomorphism. In this work, we analyze the expressive power of GNNs with random node (RNI) We prove that these models are universal, a first such result for GNNs not relying on computationally demanding higher-order properties.
  arXiv  Detail & Related papers  (2020-10-02T19:53:05Z)
• Fast Learning of Graph Neural Networks with Guaranteed Generalizability: One-hidden-layer Case [93.37576644429578]
  Graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice. We provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems.
  arXiv  Detail & Related papers  (2020-06-25T00:45:52Z)
• Eigen-GNN: A Graph Structure Preserving Plug-in for GNNs [95.63153473559865]
  Graph Neural Networks (GNNs) are emerging machine learning models on graphs. Most existing GNN models in practice are shallow and essentially feature-centric. We show empirically and analytically that the existing shallow GNNs cannot preserve graph structures well. We propose Eigen-GNN, a plug-in module to boost GNNs ability in preserving graph structures.
  arXiv  Detail & Related papers  (2020-06-08T02:47:38Z)
• Generalization and Representational Limits of Graph Neural Networks [46.20253808402385]
  We prove that several important graph properties cannot be computed by graph neural networks (GNNs) that rely entirely on local information. We provide the first data dependent generalization bounds for message passing GNNs. Our bounds are much tighter than existing VC-dimension based guarantees for GNNs, and are comparable to Rademacher bounds for recurrent neural networks.
  arXiv  Detail & Related papers  (2020-02-14T18:10:14Z)

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.