Localized Heat Kernel for Graph Neural Networks

Abstract

Graph Neural Networks (GNNs) with heat kernel effectively capture the smoothness of labels and features across nodes, preventing oscillations during propagation, and denoising the graph. However, existing models typically employ a global heat kernel, where the diffusion process depends on a single, uniform diffusion time, inevitably resulting in over-smoothing. Additionally, the global heat kernel struggles to handle heterophilic graphs, where nodes exhibit varying neighbor label distributions. To address the above issues, we extend the global heat kernel by a localized scale (i.e., node-level) and integrate it with graph convolution, yielding the Localized Heat Kernel for GNN (LHK-GNN). By adaptively adjusting the diffusion time for each node, our approach enables heat diffusion to accommodate local complexity on graph. Experiments demonstrate the effectiveness of LHK-GNN in mitigating over-smoothing and handling heterophilic graphs.