A unified theory of context-conditioned efficient and predictive coding

Sensory processing does not occur in isolation: what neurons represent in a given sensory modality is shaped by signals from other senses, actions, and behavioral context. This context dependence raises a fundamental question for theories of neural coding: how can circuits efficiently encode their local input while using information available elsewhere in the brain? Here we develop a unified theory of efficient and predictive coding that shows how multimodal contextual information can optimize representations within a local sensory circuit. We demonstrate analytically that the efficient-coding solution maps onto an interpretable neural algorithm: contextual signals provide expectations about the sensory input to the local circuit, local neurons encode deviations from those expectations, and recurrent interactions whiten the residual signals. This result establishes a mathematical equivalence between context-conditioned efficient coding and predictive coding, revealing that predictive computations can emerge from efficient input compression guided by context. The resulting framework is distinct from both classical redundancy reduction within a single modality and hierarchical Bayesian inference. The theory explains and unifies diverse experimental phenomena, including cross-modal suppression of responses to predicted inputs and multimodal receptive fields across sensorimotor, audiovisual, visual-olfactory, and auditory-somatosensory circuits, while recovering classical unimodal coding effects as limiting cases. By linking coding objectives, circuit mechanisms, and experimentally observed phenomena within a single analytical framework, this work provides a principled foundation for understanding how distributed neural systems use context to shape local representations.