arXiv Machine Learning By Jiasong Han, Yunkai Chai, Jintao Wang

A Positional Realizability Theory of Length Generalization in Single-Head Attention

Read the original on arXiv Machine Learning →

arXiv:2610. 41218v1 Announce Type: new Abstract: Why does length generalization (LG) depend so sharply on the positional encoding (PE)?

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arXiv AI
Oct 27

Relational Composition as Parallel Transport: What Per-Entity Frames Force in Attention

The paper investigates how treating each entity in a graph or language model as having its own coordinate frame—viewed as a symmetry—constrains the form of attention mechanisms. It shows that with orthogonal transports, invariant attention scores depend only on norms and transported inner products, while equivariant messages lie in the span of the entity vectors and their transported counterparts. The authors demonstrate that standard attention corresponds to a flat shared frame, and that incorporating per‑entity frames allows relations to be represented as operators that compose via parallel transport, yielding empirical gains on synthetic relational tasks and natural language benchmarks.

By Aakash Sarkar, Ananya Mukherjee, Motoshige Sato