mlsanityData to 7 Oct 2026

FloydNet: A Learning Paradigm for Global Relational Reasoning

arXiv 2601.19094 ↗First posted 27 Jan 2026cs.LG cs.AIcited by 1

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Abstract (arXiv)

Learning algorithmic computation often requires explicit relational intermediate states, yet many graph processors maintain their primary states on individual entities. We introduce fnet and 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 kfnetk 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 kfnetk 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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 53 of its 80 references that are in the map. First posted on arXiv 27 Jan 2026.

Builds on

53 of 80 references.

References · 53

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Citing papers per year: 2026: 1.

1 paper.

  1. 2026Algorithmic Task Capture, Computational Complexity, and Inductive Bias of Infinite Transformerscited by 1