Energy Guided smoothness to improve Robustness in Graph Classification
Abstract
Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to generalise on low-order graphs, low label coverage, or when a model is over-parameterized. We establish both empirical and theoretical links between GNN robustness and the reduction of the total Dirichlet Energy of learned node representations, which encapsulates the hypothesized GNN smoothness inductive bias. Finally, we introduce two training strategies to enhance GNN robustness: (1) by incorporating a novel inductive bias in the weight matrices through the removal of negative eigenvalues, connected to Dirichlet Energy minimization; (2) by extending to GNNs a loss penalty that promotes learned smoothness. Importantly, neither approach negatively impacts performance in noise-free settings, supporting our hypothesis that the source of GNNs robustness is their smoothness inductive bias.
Cite
@article{arxiv.2412.08419,
title = {Energy Guided smoothness to improve Robustness in Graph Classification},
author = {Farooq Ahmad Wani and Maria Sofia Bucarelli and Andrea Giuseppe Di Francesco and Oleksandr Pryymak and Fabrizio Silvestri},
journal= {arXiv preprint arXiv:2412.08419},
year = {2026}
}