RayE-Sub: Countering Subgraph Degradation via Perfect Reconstruction

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.