Unveiling Mode Connectivity in Graph Neural Networks

2025-02-18

AI Summary

This work presents the first systematic investigation of mode connectivity in the loss landscape of Graph Neural Networks (GNNs), revealing its nonlinear, graph-structure-dependent nature—particularly governed by graph homophily—and thereby filling a key theoretical gap. Methodologically, it integrates loss landscape analysis, empirical mode connectivity verification, graph statistical modeling, and generalization error theory to derive a novel generalization bound grounded in loss barrier metrics. The contributions are threefold: (1) It establishes that GNN mode connectivity is fundamentally determined by graph properties—not model architecture—distinguishing it markedly from CNNs and MLPs; (2) It demonstrates a strong empirical and theoretical correlation between mode connectivity and generalization performance, substantiating its utility as an interpretable diagnostic tool; (3) It provides new theoretical foundations and practical guidance for optimizing GNN training and enabling domain adaptation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

A fundamental challenge in understanding graph neural networks (GNNs) lies in characterizing their optimization dynamics and loss landscape geometry, critical for improving interpretability and robustness. While mode connectivity, a lens for analyzing geometric properties of loss landscapes has proven insightful for other deep learning architectures, its implications for GNNs remain unexplored. This work presents the first investigation of mode connectivity in GNNs. We uncover that GNNs exhibit distinct non-linear mode connectivity, diverging from patterns observed in fully-connected networks or CNNs. Crucially, we demonstrate that graph structure, rather than model architecture, dominates this behavior, with graph properties like homophily correlating with mode connectivity patterns. We further establish a link between mode connectivity and generalization, proposing a generalization bound based on loss barriers and revealing its utility as a diagnostic tool. Our findings further bridge theoretical insights with practical implications: they rationalize domain alignment strategies in graph learning and provide a foundation for refining GNN training paradigms.

Problem

• Explore mode connectivity in GNNs
• Analyze graph structure impact on connectivity
• Link mode connectivity to generalization performance

Innovation

• Explores mode connectivity in GNNs
• Links graph structure to connectivity
• Proposes generalization bound tool