Latent Coherence: Do Frontier Language Models' Probability Judgments Obey the Law of Total Probability?
arXiv:2610.31833v1 Announce Type: new Abstract: LawZero's Scientist AI trains a Predictor toward the Bayesian posterior, with an objective that penalizes inconsistent probabilities among latent explanations. We ask whether current frontier language models, with no such training, are already consistent in this sense zero-shot: do their probability judgments satisfy the law of total probability, $P(X)=\sum_z P(z)P(X|z)$, when the latent $z$ must be inferred from records in the context? In separate single-turn calls, models are asked for $P(X)$, for $P(z)$ over the latent's states, and for $P(X|z)$; a causal family applies the same test to $P(y|do(x))$ and the back-door adjustment. Every query has an exact ground-truth probability, and a subset of items is asked in three wordings to separate