arXiv cs.CL· Abraham Chachamovits·· 2 天前AI 评分12
来自 Bethe-Ansatz 的早期 Token 相关性：面向并行提议的边际保持构造
A Bethe-Ansatz Source of Early Token Correlations: A marginal-preserving construction for parallel proposals
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研究者从周期性 XXZ 链构造出坐标 Bethe-Ansatz 概率律，并与相同一、二位点矩下的最大熵成对投影对比。在八位点三激发扇区中，对称性使全概率律差异降为一维，由连续三位点矩 δ 决定，该差异在 Δ=(3+√3)/2 处变号并恰好消失。
正文 · 原文
Abstract:Parallel token proposals need a joint law, not merely accurate token marginals. We construct coordinate-Bethe-ansatz laws from the periodic XXZ chain and compare them with their maximum-entropy pairwise projections at identical one- and two-site moments. In an eight-site, three-excitation sector, symmetry makes the full probability-law difference one-dimensional, determined by a contiguous three-site moment $\delta$. Along the Bethe branch, this gap changes sign and vanishes exactly at $\Delta=(3+\sqrt3)/2$, where the eigenstate law becomes pairwise. A nonlinear two-token readout preserves separate token marginals yet exposes a distance $2|\delta|$; a direct three-token readout preserves all one- and two-token marginals yet exposes $4|\delta|$. At $\Delta=1.5$ these deterministic binary distances are $0.02654573$ and $0.05309145$. We give an exact target-alignment formula and prove a strict speculative accepted-prefix advantage throughout an unrestricted open neighborhood of a constructed target. These are finite-law existence results, not measured language-model or wall-clock gains.
| Comments: | 6 pages, 2 tables. Ancillary files reproduce the numerical results |
| Subjects: | Computation and Language (cs.CL); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.16781 [cs.CL] |
| (or arXiv:2610.16781v2 [cs.CL] for this version) | |
| https://doi.org/10.48550/arXiv.2610.16781 arXiv-issued DOI via DataCite |
Submission history
From: Abraham Chachamovits [view email]
[v1]
Mon, 12 Oct 2026 13:38:31 UTC (16 KB)
[v2]
Wed, 14 Oct 2026 20:07:58 UTC (22 KB)
来源：arXiv cs.CL · arxiv.org