AI 中文总结
研究如何编排采样器适应机制，提出通用热身路径，用与采样器无关的指南针及各路线自身度量，基于证据路由，规则与采样器无关，实验显示自动热身性能优于其他方法，指向采样器超参数调整的连贯理论。
AI 中文摘要
采样器转换是局部的，但其效率受全局后验几何控制。热身通过调整步长、度量等进行衔接。目前这些适应机制的编排常通过固定时间表和启发式选择。我们将编排重塑为既定预算内基于证据的路由。通用热身路径使用一个与采样器无关的指南针，允许各路线采用自身度量。其规则与采样器无关，通过标量门评估基于梯度的HMC族实现。该设计给出吸引子保证，有限转录界限限制证据。实验表明自动热身优于预声明的Fisher低秩主方法，还改进了每梯度的有效样本量。此路径指向采样器超参数调整的连贯理论。
英文摘要
Euclidean Hamiltonian Monte Carlo (HMC) warmup must choose a step size and constant preconditioner from limited, nonstationary draws. Standard warmup follows a fixed schedule and generally requires the preconditioner structure to be specified in advance. We present a multi-chain controller that starts diagonal and, at dimension-derived window endpoints, selects between diagonal and low-rank-plus-diagonal inverse mass matrices and chooses the retained rank, subject to dimension and sample-support caps. When evidence is inconclusive, the controller gathers another scheduled window. Persistent within-/between-chain disagreement means draws do not support treating one constant preconditioner as an adequate global description; the controller retains its within-region matrix and advises a population or tempering method for regional exploration. Poor held-out score--position linearity advises reparameterization. The controller selected low rank in every evaluated headline benchmark NUTS run ($12/12$). Geometric-mean pooled ESS-per-gradient ratios relative to the prespecified Fisher low-rank warmup and Welford diagonal warmup baselines were respectively $2.451$ and $22.572$ on the synthetic ill-conditioned Gaussian benchmark, and $1.951$ and $6.264$ on the German-credit Bayesian logistic-regression posterior; all compared runs passed the post-warmup quality check. This method unifies common HMC warmup heuristics in one evidence-driven controller, reducing manual choices and turning warning signals into actionable guidance.
