Graph Distillation with Eigenbasis Matching
This addresses the challenge of computational efficiency in graph data processing for machine learning practitioners, but it is incremental as it builds on existing graph distillation techniques.
The paper tackles the problem of efficiently training graph neural networks (GNNs) by distilling a small synthetic graph to replace large real graphs, and the result is that their method, GDEM, outperforms state-of-the-art graph distillation methods with significant distillation efficiency and cross-architecture generalization ability.
The increasing amount of graph data places requirements on the efficient training of graph neural networks (GNNs). The emerging graph distillation (GD) tackles this challenge by distilling a small synthetic graph to replace the real large graph, ensuring GNNs trained on real and synthetic graphs exhibit comparable performance. However, existing methods rely on GNN-related information as supervision, including gradients, representations, and trajectories, which have two limitations. First, GNNs can affect the spectrum (i.e., eigenvalues) of the real graph, causing spectrum bias in the synthetic graph. Second, the variety of GNN architectures leads to the creation of different synthetic graphs, requiring traversal to obtain optimal performance. To tackle these issues, we propose Graph Distillation with Eigenbasis Matching (GDEM), which aligns the eigenbasis and node features of real and synthetic graphs. Meanwhile, it directly replicates the spectrum of the real graph and thus prevents the influence of GNNs. Moreover, we design a discrimination constraint to balance the effectiveness and generalization of GDEM. Theoretically, the synthetic graphs distilled by GDEM are restricted spectral approximations of the real graphs. Extensive experiments demonstrate that GDEM outperforms state-of-the-art GD methods with powerful cross-architecture generalization ability and significant distillation efficiency. Our code is available at https://github.com/liuyang-tian/GDEM.