Unassigned · 2026-10-07
When Can World Models Recover Physical Laws?
Ye Yuan, Jun Liu
AI-assisted summary based on the paper. Consult the linked source for methods and limitations. Benchmark numbers appear after editor verification.
TL;DR
The authors argue that accurate prediction from a fixed recording does not guarantee recovery of the underlying physical law because distinct dynamics can produce identical observations under the same allowed experiments. They formalize law recovery on a fixed domain with sensor uncertainty and an acquisition budget, derive information-theoretic distinguishability conditions, give a decoding construction, and quantify minimax acquisition costs for Lipschitz dynamics from noisy full-state readouts after resets.
Why it matters
The paper separates “prediction agreement” from “physical-law identifiability,” and gives explicit conditions on which experiments make different laws distinguishable to a target accuracy under noise and budget constraints. It provides information-theoretic necessary conditions (via rate–distortion converse) and constructive recovery (finite response codebook), plus stability via an inverse response modulus. The cost results quantify how preparation/readout choices affect the budget needed for uniform law error.
Method
- Model recovery as estimating a physical field F_w over a fixed compact evaluation domain from an apparatus that can execute episodes (preparation, inputs, readout schedule) under sensor noise and a total acquisition budget.
- Define experiment equivalence w~_A v via identical response distributions/means for all permitted episodes (including adaptive policies); a positive ambiguity floor κ_A limits achievable recovery.
- Use information theory (rate–distortion converse) to relate required description information to apparatus information, then construct a finite response codebook decoder and quantify stability via an inverse response modulus; specialize to Lipschitz fields to obtain minimax budget rates under different readouts.
Limitation
The evidence in the report supports the stated mathematical mechanisms and the implemented estimators using synthetic or reproducible cases; it does not certify a learned controller for physical deployment.
Abstract (from arXiv)
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 $\Theta(\varepsilon^{-(d+4)/2})$ for squared law error $\varepsilon$, compared with $\Theta(\varepsilon^{-(d+2)/2})$ 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.
Related papers
- Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physics
- MultiEcho: An Experimental Science of Learned Worlds
- ALDER: Discovering the Laws of a World by Acting in It
- Counterfactual Action Evaluation, Observation Bottlenecks, and Representation Geometry in Joint-Embedding Predictive World Models
- World Models' Last Exam in Physics
Publication record
Bibliographic evidence describes where and when a record appeared. It does not validate scientific claims.
First public release: 2026-09-15 · Indexed by Pub-AI: 2026-10-07 UTC
When Can World Models Recover Physical Laws?
Preprint posted: 2026-09-15 · Original record ↗
- arxiv
- 2610.06877
Explicit source versions (1)
- v1 · 2026-09-15
- Preprint available
Source date: 2026-09-15 · First detected: 2026-10-25 UTC · Historical baseline
Source evidence (1)
- Official evidence ↗ · atom:published (official metadata)
Abstract · arxiv
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.