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About this paper
Yan Wang, Chuan-Xian Ren
PairAlign introduces a pair-centric graph rewiring framework that addresses over-squashing in message-passing neural networks by identifying and reducing specific pairwise communication shortages. The method employs an Optimal Transport-guided strategy to coordinate the allocation of a finite rewiring budget, resulting in improved performance on node and graph classification tasks across diverse MPNN backbones.
Key insights
- Over-squashing can be precisely formulated and diagnosed as a 'pairwise communication shortage,' providing an interpretable, pair-level metric that correlates strongly with Jacobian-based influence and effective resistance.
- Adding new edges for graph rewiring has a non-monotone effect: while it creates new paths, it can simultaneously dilute existing propagation mass due to normalization, necessitating careful re-evaluation of shortage during the process.
- Optimal Transport provides a 'coverage advantage' for allocating rewiring budgets, enabling the distribution of a finite budget broadly and effectively across diverse shortage targets rather than concentrating on a few locally 'cheapest' repairs.
Summary by alphaXiv.
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