Beyond the Laplacian: Doubly Stochastic Matrices for Graph Neural Networks
Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the inverse of the modified Laplacian, to naturally encode continuous multi-hop proximity and strict local centrality. To overcome the intractable $O(n^3)$ complexity of exact matrix inversion, we first utilize a truncated Neumann series to scalably approximate the DSM, which serves as the foundation for our proposed DsmNet. Furthermore, because algebraic truncation inherently causes probability mass leakage, we introduce DsmNet-compensate. This variant fe...
| Authors | Zhaobo Hu, Vincent Gauthier, Mehdi Naima |
|---|---|
| Primary category | cs.LG |
| Published | 16 April 2026 |
| Last updated at source | 16 April 2026 |
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