RayE-Sub: Countering Subgraph Degradation via Perfect Reconstruction

Kuo Yang, Zhengyang Zhou, Xu Wang, Pengkun Wang, Limin Li, Yang Wang

Abstract: Subgraph learning has dominated most practices of improving the expressive power of Message Passing Neural Networks (MPNNs). Existing subgraph discovery policies can be classified into node-based and partition-based, which both achieve impressive performance in most scenarios. However, both mainstream solutions still face a subgraph degradation trap. Subgraph degradation is reflected in the phenomenon that the subgraph-level methods fail to offer any benefits over node-level MPNNs. In this work, we empirically investigate the existence of the subgraph degradation issue and introduce a unified perspective, perfect reconstruction, to provide insights for improving two lines of methods. We further propose a subgraph learning strategy guided by the principle of perfect reconstruction. To achieve this, two major issues should be well-addressed, i.e., (i) how to ensure the subgraphs to possess with ‘perfect’ information? (ii) how to guarantee the ‘reconstruction’ power of obtained subgraphs? First, we propose a subgraph partition strategy Rayleigh-resistance to extract non-overlap subgraphs by leveraging the graph spectral theory. Second, we put forward a Query mechanism to achieve subgraph-level equivariant learning, which guarantees subgraph reconstruction ability. These two parts, perfect subgraph partition and equivariant subgraph learning are seamlessly unified as a novel Rayleigh-resistance Equivariant Subgraph learning architecture (RayE-Sub). Comprehensive experiments on both synthetic and real datasets demonstrate that our approach can consistently outperform previous subgraph learning architectures.