Reconciling time and prediction error theories of associative learning

Learning involves forming associations between sensory events that have a consistent temporal relationship. Influential theories based on prediction errors explain numerous behavioral and neurobiological observations but do not account for how animals measure the passage of time. Here, we propose a Bayesian theory for temporal causal learning, where the structure of inter-stimulus intervals is used to infer the singular cause of a rewarding stimulus. We show that a single assumption of timescale invariance, formulated as an hierarchical generative model, is sufficient to explain a puzzling set of learning phenomena, including the power-law dependence of acquisition on inter-trial intervals and timescale invariance in response profiles. A biologically plausible algorithm for inference recapitulates salient aspects of both timing and prediction error theories. The theory predicts neural signals with distinct dynamics that encode causal associations and temporal structure.