模型在临界平衡时产生类直觉行为，能发现新策略。
Intuition emerges in Maximum Caliber models at criticality
- 通过最大作用量原理与控制参数λ，让模型在记忆与想象间找平衡。
- 在随机迷宫中训练时，高λ下出现规则破坏性幻觉，临界区涌现新策略。
- 适合研究模型认知机制或智能涌现的学者关注。
大型预测模型是否仅复述训练数据，还是具备真正洞察，尚无物理解释。本文发现一种原始的直觉机制：在学习过程中形成一种亚稳态相，该相在下一词预测与未来路径熵之间达到临界平衡。这一机制通过‘心智调优’（mind-tuning）被揭示，即在预测模型中引入最大作用量原理，并以类似温度的控制参数λ进行调控。在确定性迷宫中的随机游走训练中，模型展现出丰富的相图：低λ时为模仿行为，高λ时出现规则破坏性幻觉，中间存在一个脆弱窗口，表现出强协议依赖性（滞后现象）和多稳定性，模型在此区间可自发发现新的目标导向策略。这些现象可由一个有效低维理论描述，将直觉定义为在记忆现实与想象可能之间临界平衡下的涌现属性。
原文摘要 · Abstract (English)
Whether large predictive models merely parrot their training data or produce genuine insight lacks a physical explanation. This work reports a primitive form of intuition that emerges as a metastable phase of learning that critically balances next-token prediction against future path-entropy. The intuition mechanism is discovered via mind-tuning, the minimal principle that imposes Maximum Caliber in predictive models with a control temperature-like parameter $λ$. Training on random walks in deterministic mazes reveals a rich phase diagram: imitation (low $λ$), rule-breaking hallucination (high $λ$), and a fragile in-between window exhibiting strong protocol-dependence (hysteresis) and multistability, where models spontaneously discover novel goal-directed strategies. These results are captured by an effective low-dimensional theory and frame intuition as an emergent property at the critical balance between memorizing what is and wondering what could be.
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