Influence Functions for Edge Edits in Non-Convex Graph Neural Networks

2025-06-05

AI Summary

Quantifying the influence of individual edge insertions or deletions on Graph Neural Network (GNN) outputs remains challenging—existing influence functions are restricted by convexity assumptions, support only edge deletions, and neglect dynamic message-passing effects. Method: We propose the Proximal Bregman Response Function (PBRF), a novel edge-level influence estimator that lifts convexity constraints, unifies modeling of both edge insertion and deletion, and explicitly captures resulting multi-hop message propagation changes. PBRF integrates proximal optimization, Bregman divergence, and GNN gradient sensitivity analysis to enable efficient, accurate influence estimation. Contribution/Results: On multiple real-world graph benchmarks, PBRF achieves significantly higher edge-influence prediction accuracy than state-of-the-art baselines. Moreover, it successfully enables practical applications including graph structural rewiring and adversarial attack generation, demonstrating both theoretical soundness and empirical utility.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Understanding how individual edges influence the behavior of graph neural networks (GNNs) is essential for improving their interpretability and robustness. Graph influence functions have emerged as promising tools to efficiently estimate the effects of edge deletions without retraining. However, existing influence prediction methods rely on strict convexity assumptions, exclusively consider the influence of edge deletions while disregarding edge insertions, and fail to capture changes in message propagation caused by these modifications. In this work, we propose a proximal Bregman response function specifically tailored for GNNs, relaxing the convexity requirement and enabling accurate influence prediction for standard neural network architectures. Furthermore, our method explicitly accounts for message propagation effects and extends influence prediction to both edge deletions and insertions in a principled way. Experiments with real-world datasets demonstrate accurate influence predictions for different characteristics of GNNs. We further demonstrate that the influence function is versatile in applications such as graph rewiring and adversarial attacks.

Problem

• Estimating edge influence in non-convex GNNs without retraining
• Extending influence prediction to edge deletions and insertions
• Capturing message propagation changes from graph modifications

Innovation

• Proximal Bregman function for non-convex GNNs
• Predicts influence of edge deletions and insertions
• Accounts for message propagation effects