Probabilistically Rewired Message-Passing Neural Networks
This work addresses a key bottleneck in graph neural networks for researchers and practitioners by providing a principled method to infer graph structures, though it appears incremental as it builds on existing MPNN frameworks.
The authors tackled the problem of fixed graph structures in message-passing neural networks (MPNNs), which can cause issues like over-squashing and limited expressive power, by introducing probabilistically rewired MPNNs (PR-MPNNs) that learn to add relevant edges and omit less beneficial ones, resulting in competitive or superior predictive performance on real-world datasets compared to traditional MPNNs and graph transformers.
Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable $k$-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.