Measuring Coherence in Predictive Models

Many decision making procedures that make use of probabilistic predictors assume that training on new data acts as Bayesian conditioning. When this assumption breaks, the downstream procedure can perform poorly. E.g. we show that in active learning, incoherent updates cause the procedure to prefer to acquire suboptimal points. To quantify how far a model's predictive updates depart from conditioning, we introduce the _incoherence ratio_. We empirically find that amortised predictors such as TabPFN can be more coherent than standard parametric approximations to Bayesian inference. In synthetic active learning experiments, more coherent models acquire better data, an effect not attributable to better predictive performance. In many tasks, decisions depend on a predictor only through its induced action. We therefore introduce action coherence, a decision-theoretic relaxation that measures only the incoherence affecting that action. These diagnostics make coherence testable and quantifiable, enabling incoherence to be diagnosed and addressed.