发表机构
Huazhong University of Science and Technology; University of Waterloo（华中科技大学; 滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究世界模型何时能恢复物理定律，提出率失真框架和实验可区分性条件，并给出Lipschitz场下的最小最大采样预算，揭示干预、校准和重复测量的作用。
AI 中文摘要
准确的预测并不能证明世界模型已经恢复了物理定律：在相同的观测协议下，不同的动力学可以生成相同的记录。我们在一个固定的物理域上，在明确的实验目录、传感器不确定性和采集预算下，形式化了定律恢复问题。率失真逆定理将描述定律所需的信息与设备能够揭示的信息区分开来。其构造性对应部分给出了一个有限的响应码本和一个明确的解码预算。在紧致的世界类别上，当且仅当每对不同的定律在实验上可区分时，均匀恢复是可能的；等价地，设备可以恢复每个有限定律源的熵。一个逆响应模量量化了稳定性。对于在$d$维状态-动作域上的Lipschitz场，重置后的带噪全状态读数要求平方定律误差$\varepsilon$的最小最大预算$\Theta(\varepsilon^{-(d+4)/2})$，而直接场观测则需要$\Theta(\varepsilon^{-(d+2)/2})$。精确的穿越时间对称性在自适应实验选择和任意持续时间及恒定输入下建立了下界。可重复的合成案例说明了干预、校准和重复测量的各自作用。总之，这些结果确定了哪些证据支持物理定律恢复的主张以及获取这些证据的成本。
英文摘要
Accurate prediction does not establish that a world model has recovered a physical law: distinct dynamics can generate identical records under the same observation protocol. We formulate law recovery on a fixed physical domain under an explicit catalog of experiments, sensor uncertainty, and an acquisition budget. A rate--distortion converse separates the information needed to describe a law from the information the apparatus can reveal. Its constructive counterpart gives a finite response codebook and an explicit decoding budget. On compact world classes, uniform recovery is possible exactly when every pair of different laws is experimentally distinguishable; equivalently, the apparatus can recover all the entropy of every finite law source. An inverse response modulus quantifies stability. For Lipschitz fields on a $d$-dimensional state--action domain, noisy full-state readouts after resets require minimax budget $Θ(\varepsilon^{-(d+4)/2})$ for squared law error $\varepsilon$, compared with $Θ(\varepsilon^{-(d+2)/2})$ for direct field observations. Exact crossing-time symmetries establish the lower bound under adaptive experiment selection and arbitrary durations with constant inputs. Reproducible synthetic cases illustrate the separate roles of intervention, calibration, and repeated measurement. Together, the results identify which evidence supports a claim of physical-law recovery and the cost of acquiring it.
