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Life sciences · Preprint
arXiv · August 11, 2026
Posted before peer review. The findings may change or fail to hold.
PairAlign is a novel graph rewiring algorithm designed to mitigate over-squashing in message-passing neural networks by identifying and rewiring pairwise communications whose demand is poorly supported by graph topology. The method combines theoretical justification (Jacobian-based shortage proxy, optimal transport allocation) with empirical validation on standard benchmarks, but has not undergone peer review and generalisability to downstream applications is not established.
Preprint. Intervention: PairAlign: a pair-centric graph rewiring framework using demand-support shortage scoring and Optimal Transport-guided edge allocation..
PairAlign combines original-graph structural demand with current-graph finite-hop propagation support to identify interactions whose communication demand is poorly supported by topology. Theory shows demand-support shortage score provides a computable proxy for Jacobian-based shortage with pair-level interpretation of over-squashing. Edge insertion has a two-sided effect: creates useful walks while simultaneously diluting normalized transition mass.
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This is an unrefereed preprint presenting a novel algorithmic framework with theoretical analysis and experimental validation, but lacking peer review and clinical or established-domain validation.
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Message-passing neural networks (MPNNs) often struggle when task-relevant information is distributed across distant regions of a graph, since local propagation must compress remote signals through limited structural interfaces. Graph rewiring provides a structural response to over-squashing. Most existing methods rely on edge-level bottleneck scores or graph-level connectivity surrogates. With a limited rewiring budget, the key question is which pairwise communications most need structural support. This paper proposes PairAlign, a pair-centric graph rewiring framework that makes this question explicit through demand-support shortage. Specifically, PairAlign combines original-graph structural demand with current-graph finite-hop propagation support; their ratio highlights interactions whose communication demand is poorly supported by topology, and our theory shows that this score provides a computable proxy for the corresponding Jacobian-based shortage with a pair-level interpretation of over-squashing. Our theory reveals a two-sided effect of edge insertion: a new edge can create useful walks and simultaneously dilute existing normalized transition mass. Guided by this observation, PairAlign optimizes shortage to favor edge additions that alleviate over-squashing. Beyond selecting useful additions, PairAlign further introduces an Optimal Transport-guided rewiring mechanism to coordinate the finite edge budget for pair-level structural compatibility and shortage-target coverage. It formulates communication alignment between the candidate edge budget and the shortage targets, and the theory shows that this allocation covers shortage targets more broadly and effectively than a greedy-local assignment. Experiments on standard graph benchmarks show PairAlign's improvement across message-passing backbones, validating pair-level repair as an effective route for alleviating over-squashing.
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