Learning Reusable Inference Across Representations

Good in-context prediction does not establish whether a model has learned inference that transfers across representations. We construct a controlled test using latent parity tasks whose full-rank binary embeddings change representation reuse while preserving the Bayes problem and the statistical value of joint evidence. An exact hierarchy of support-label interactions quantifies this value: at latent rank $r$, Bayes prediction needs $O(r)$ supports and polynomial-time inference, whereas the optimal label-additive predictor needs $\Theta (2^r)$ supports at fixed risk. Across two contextual architectures, final-answer training exploits more of this opportunity with persistent embeddings, but that benefit transfers incompletely to unseen embeddings. Controls show that joint-label dependence is learnable when the organisation of the evidence is supplied; difficulty at higher ranks even with persistent embeddings motivates supervision of the inference process. A process-supervised recurrent learner executes autonomously under fresh embeddings, transfers beyond its training ranks, and turns additional supports into lower risk. These results separate statistical opportunity, representation reuse, and acquired computation, showing why evaluations of learned adaptation should test both what transfers and how effectively additional context is used.