Certified World Models: Predictability Across Configuration, Horizon, and Resolution
TLDR
This paper provides predictability certificates for equivariant latent world models, analyzing error propagation across configuration, horizon, and resolution using Lyapunov spectra.
Reasoning
Strengths include rigorous theoretical results (Theorems A and B) and empirical validation on a 40-dimensional learned model with high R^2. Weaknesses are the restriction to exact equivariance and lack of real-world experiments or benchmarks.
Read-first score
Read-first score 50.5, weighted from topical fit, citation, graph, method, reproducibility, and recency signals. Original total remains 23.
Field roles
Rank sensitivity
Stability: volatile; rank range: 337.
Keyword Scores
Deep Analysis
Innovations
- Predictability certificate for equivariant latent world models: a computable region spanning configuration, horizon, and resolution.
- Theorem A: Under exact equivariance, rollout error is invariant over the monoid generated by k primitive symmetries and certified from the k generators.
- Lemma 2: Universal orbit-flatness over equivariant targets characterizes equivariance at the function level, showing unconstrained architectures cannot certify the property by construction.
- Theorem B: Approximate orbit-transfer defects propagate by the finite-time Lyapunov spectrum: expanding channels give logarithmic horizon, neutral channels accumulate linearly, contracting channels accumulate a bounded nonzero floor.
- Exact conserved charge values are certified to all horizons only at zero defect; with one-step defect η, charge-value error grows at most Tη.
- Empirical recovery of full Lyapunov spectrum (R²=0.98-0.99) on a 40-dimensional learned model using a Z_N-equivariant network, where dense and recurrent baselines fail.
- Cone/adapted-metric certificate reads an a-priori horizon off the model's own Jacobian, tight on uniformly hyperbolic dynamics and self-abstaining elsewhere, improving budgeted re-observation decisions.
- For public non-equivariant world models, the tangent spectrum gives a training-free candidate horizon, paired with a held-out divergence cross-check that abstains or corrects when the learned loop over-promises.
Methodology
The paper proposes certified world models using equivariant latent dynamics. It provides theoretical certificates (Theorems A and B) for predictability across configuration, horizon, and resolution. Empirically, it evaluates on a 40-dimensional learned model using Z_N-equivariant networks, comparing to dense and recurrent baselines, and measures Lyapunov spectrum recovery. It also introduces a cone/adapted-metric certificate and a training-free candidate horizon for non-equivariant models.
Key Results
On a 40-dimensional learned model, a Z_N-equivariant network recovers the full Lyapunov spectrum with R²=0.98-0.99, while dense and recurrent baselines fail. The cone/adapted-metric certificate provides an a-priori horizon that improves budgeted re-observation decisions.
Limitations
- Exact equivariance required for Theorem A; approximate defects propagate via Lyapunov spectrum.
- Certificate for exact conserved charge values only at zero defect; with one-step defect, error grows at most Tη.
- Cone/adapted-metric certificate is tight only on uniformly hyperbolic dynamics; self-abstains elsewhere.
- For non-equivariant models, the tangent spectrum gives a candidate horizon but requires a held-out divergence cross-check to abstain or correct when over-promising.
- Unconstrained architectures cannot certify predictability by construction (Lemma 2).