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

A proximal Bregman response function enhances non-convex graph neural networks, improving edge influence prediction accuracy. This unified approach addresses limitations by considering edge insertions and message propagation changes, offering interpretability and robustness. Applied to analyze edge rewiring, identify adversarial edits, and assess node classification, it demonstrates high correlation between estimated and actual influence. The analysis on a four-layer GCN across Influence, CiteSeer, and PubMed shows strong correlations (0.94-0.98). Two-layer ChebNet and GAT models exhibit correlations (0.8-0.99) and Dirichlet Energy (0.8-0.94). The study validates the effectiveness of the function in deletion and insertion scenarios, with 143 out of 200 inserted edges reducing over-squashing. However, validation loss and over-smoothing may not improve. Conducted on a four-layer GCN model trained on the Texas dataset, experiments were performed on various GPUs with model hyperparameters tuned over a specific search space.