A Bethe-Ansatz Source of Early Token Correlations: A marginal-preserving construction for parallel proposals
Read the original on arXiv Machine Learning →The paper constructs coordinate‑Bethe‑Ansatz joint laws for parallel token proposals using the periodic XXZ chain and compares them to maximum‑entropy pairwise projections that match the same one‑ and two‑site moments. In an eight‑site, three‑excitation sector, symmetry reduces the difference between the full probability law and its pairwise projection to a single contiguous three‑site moment δ, which changes sign and vanishes at Δ=(3+√3)/2, making the eigenstate law pairwise. Nonlinear two‑token and three‑token readouts preserve token marginals while revealing distances proportional to |δ|, with explicit deterministic binary distances computed at Δ=1.5; the authors also provide an exact target‑alignment formula and prove a strict speculative accepted‑prefix advantage in an unrestricted open neighborhood of the constructed target.
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