An Omitted Mode Is a Rare Rule: The Sampling-Verification Danger Law in Continuous Code World Models
arXiv:2608.17956
2026
Theory
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
This paper provides a concrete mathematical account of why finite transition verification can certify a continuous world model while completely missing a rare hybrid mode. The key transferable assets are the exact miss probability for independent gates, the risk factorization under independence, and a Lipschitz localization theorem converting a pointwise model error into a minimum-volume disagreement region. These results suggest verification procedures that allocate tests according to estimated event risk and explicitly search for planner-reachable rare boundaries rather than relying on uniform rollouts. The Lipschitz bound can also guide adaptive test placement and determine when a finite gate is fundamentally incapable of detecting a mode.
Ideas from this paper
✗ Failed on benchmark
2026
Replace a fixed-size random transition gate with a risk-calibrated gate whose test count is chosen from the estimated probability of a critical event and the cost of shipping a model that misses it. The gate should combine ordinary i.i.d. rollouts with planner-generated probes aimed at high-cost boundaries, because uniform sampling can make a dangerous model appear perfectly accurate.
Useful7/10
Difficulty4/10
Novelty7/10
Unverified
2026
Use the localization theorem to turn a detected pointwise simulator error into a guaranteed region that must contain similarly large error, then place verification samples inside that region instead of sampling uniformly. The same bound can guide a training regularizer: errors with large amplitude and large local Lipschitz constants are penalized because they create planner-exploitable disagreement regions.
Useful6/10
Difficulty5/10
Novelty6/10