通过匹配时空相关性，提升物理约束下的搜索效率。
Constraint-Enhanced Physical Search through Correlation Matching
- 用时间相关性驱动探索，匹配物理更新产生的空间相关性。
- 在最小化拔河老虎机模型中，效率随相关性匹配度提升而显著改善。
- 适合研究生物决策、强化学习及物理系统中的智能搜索机制。
物理系统不仅向搜索过程添加噪声，还会施加约束，生成结构化的关联。我们提出一种约束增强的物理搜索原则：探索中的时间相关性应与更新动力学中由约束诱导的空间相关性相匹配。通过一个最小化的拔河老虎机模型（TOW），我们发现守恒律可将局部观测转化为不同选项间的差异证据，而时间相关的驱动力则控制探索顺序。搜索效率的提升并非依赖更强的随机性或最大反相关性，而是取决于时间相关性与物理更新尺度的匹配，该尺度决定了反馈如何转化为证据。量纲分析表明，更新噪声与对比度之比是限制时间反相关强度的关键参数。结果揭示了一种通用的物理搜索组织原则：约束与波动可产生结构化的时空关联，当这些关联与更新动态相匹配时，高效探索便自然涌现。
原文摘要 · Abstract (English)
Physical systems do not merely add noise to search processes; they impose constraints that generate structured correlations. We propose a principle of constraint-enhanced physical search in which temporal correlations in exploration are matched to constraint-induced spatial correlations in the update dynamics. Using a minimal tug-of-war bandit model (TOW), we show that a conservation law converts local observations into differential evidence across alternatives, while a temporally correlated drive controls the order of exploration. Search efficiency is improved not by stronger randomness or by maximal anti-correlation, but by matching the temporal correlation to the physical update scale that converts feedback into evidence. A scaling estimate identifies the update-noise-to-contrast ratio as the leading parameter that limits how strongly temporal anti-correlation can be used. The results suggest a general organizing principle for physical search: constraints and fluctuations can generate structured spatiotemporal correlations, and efficient exploration emerges when these correlations are matched to the update dynamics.
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