提出新型关系推理框架，实现全局关系组合的高效学习。
FloydNet: A Learning Paradigm for Global Relational Reasoning
- 基于弗洛伊德-沃舍尔结构设计枢轴注意力机制，显式建模关系组合
- 在CLRS-30上达96.64%平均准确率，在非度量TSP上实现99.8%最优解率
- 适用于需要全局关系推理的图学习任务，如路径规划与图同构判定
学习算法计算通常需要显式的关联中间状态，但许多图处理模型仅在单个实体上维护主状态。我们提出 net和 extbf{枢轴注意力}（PA），通过维护有序对状态，利用每个枢纽节点j，从对(i,j)和(j,k)构成的候选中关注目标关系(i,k)。受弗洛伊德-沃舍尔算法的成对-枢纽结构启发，PA并行学习关系组合与枢纽加权，而非执行其有序的最小-加法递推。 net框架将此操作扩展至有序k元组，其中自注意力与PA分别为其k=1和k=2的情况。在原子元组初始化与不变读出条件下，我们证明了 net{k} 的图区分能力不强于k-FWL；在BREC数据集上，各变体均匹配对应沃尔德逻辑（WL）参考的成功集合。在报告的CLRS-30协议下， net达到96.64%的平均准确率；在未见的非度量旅行商问题实例上，使用10个样本即获得99.8%的最优解率。
原文摘要 · Abstract (English)
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.
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