Acquisition Policies Change the Bayes Rule: Policy-Conditioned Posterior Correction for Multimodal Learning

Multimodal models usually predict from available modalities as if an observed subset had fixed predictive meaning. We show that this can fail after an acquisition-policy shift. The same observed content and mask can imply a different class posterior. We formulate policy-conditioned multimodal learning and define the observed acquisition mass, the class-conditional probability that a policy produces an observed record after marginalizing unobserved content. Its ratio transforms a source posterior into a policy-specific posterior, while a posterior-weighted Jensen-Shannon divergence quantifies irreducible log-loss without policy information. Our Policy-Conditioned Observed-Mass Model (PCOM) combines a frozen source predictor, source-trained mass estimation, and policy inference from unlabeled context-mask logs. Record-level mixtures are corrected in mass space before normalization. Across CMU-MOSEI, MELD, MM-IMDb, and UPMC Food-101, PCOM improves endpoint log loss and retains positive mean gains at held-out mixture proportions. Ablations verify the roles of candidate-class conditioning and policy state, while stress tests show that state fidelity alone does not guarantee utility. Thus, policy variation should not be removed through invariance when it changes an observation's predictive meaning.