Graph Representation Learning with Laplacian Pyramid Residuals for Graph Classification

Graph neural networks have been widely used for graph classification by effectively learning local neighborhood information through message passing. However, repeated aggregation gradually smooths node representations, which drives them toward increasingly homogeneous states and diminishes subtle structural distinctions, leading to a phenomenon of oversmoothing. To cope with this problem, various methods have been explored, but they generally do not explicitly account for the structural information discarded during aggregation. This paper proposes a novel graph representation learning method with Laplacian pyramid that explicitly recovers and integrates the discarded information. At each level of the representation hierarchy, the method computes graph residuals using a difference-of-Gaussians operation adapted to graph structures, and integrates these residuals hierarchically across scales to preserve multi-level structural variations. Extensive experiments on ten standard and four large-scale graph benchmarks demonstrate that the proposed method consistently outperforms existing baselines by up to 5.5% points in classification accuracy, confirming the effectiveness of the proposed method.