FloydNet: A Learning Paradigm for Global Relational Reasoning

arXiv:2601.19094v3 Announce Type: replace-cross Abstract: Learning algorithmic computation often requires explicit relational intermediate states, yet many graph processors maintain their primary states on individual entities. We introduce fnet and extbf{Pivotal Attention} (PA), which maintain ordered pair states and update a target relation (i,k) by attending over candidates formed from (i,j) and (j,k) for every pivot j. Motivated by the pair-and-pivot structure of Floyd--Warshall, PA learns relation composition and pivot weighting in parallel rather than executing its ordered min-plus recurrence. The kfnet{k} framework extends this operation to ordered k-tuples, with Self-Attention and PA as its k=1 and k=2 cases at the attention-operation level. Under atomic tuple initialization and invariant readout, we show that kfnet{k} is no more graph-discriminative than k-FWL; on BREC, each evaluated variant matches the success set of its corresponding WL reference. fnet further achieves 96.64% mean accuracy under the reported CLRS-30 protocol and a 99.8% optimality rate with 10 samples on held-out non-metric TSP instances.

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Source: arXiv cs.AI | 2026-09-02