FloydNet: A Learning Paradigm for Global Relational Reasoning

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 \textbf{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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2601.19094 [cs.LG]

(or arXiv:2601.19094v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2601.19094 Focus to learn more arXiv-issued DOI via DataCite

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