# A Bethe-Ansatz Source of Early Token Correlations: A marginal-preserving construction for parallel proposals

arXiv: https://arxiv.org/abs/2610.16781 · HTML: https://mlsanity.com/paper/2610.16781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 6 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Parallel Token Prediction for Language Models](https://mlsanity.com/paper/2512.21323/) (2025)
- [Sequential learning on a Tensor Network Born machine with Trainable Token Embedding](https://mlsanity.com/paper/2311.05050/) (2023)

## Abstract (arXiv)

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 δ. Along the Bethe branch, this gap changes sign and vanishes exactly at Delta=(3+√3)/2, where the eigenstate law becomes pairwise. A nonlinear two-token readout preserves separate token marginals yet exposes a distance 2|δ|; a direct three-token readout preserves all one- and two-token marginals yet exposes 4|δ|. 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.