Efficient coding explains neural response homeostasis and stimulus-specific adaptation

In the absence of adaptation, the average firing rate of neurons would rise or drop when changes in the environment make their preferred stimuli more or less prevalent. However, by adjusting the responsiveness of neurons, adaptation can yield firing rate homeostasis and stabilise the average rates of neurons at fixed levels, despite changes in stimulus statistics. In sensory cortex, adaptation is typically also stimulus specific, in that neurons reduce their responsiveness to over-represented stimuli, but maintain or even increase their responsiveness to stimuli far from over-represented ones. Here, we present a normative explanation of firing rate homeostasis grounded in the efficient coding principle. Specifically, we show that this homeostasis can arise when neurons adapt their responsiveness to optimally mitigate the effect of neural noise on population coding fidelity, at minimal metabolic cost. Unlike previous efficient coding theories, we formulate the problem in a computation-agnostic manner, enabling our framework to apply far from the sensory periphery. We then apply this general framework to Distributed Distributional Codes, a specific computational theory of neural representations serving Bayesian inference. We demonstrate how homeostatic coding, combined with such Bayesian neural representations, provides a normative explanation for stimulus-specific adaptation, widely observed across the brain, and how this coding scheme can be accomplished by divisive normalisation with adaptive weights. Further, we develop a model within this combined framework, and, by fitting it to previously published experimental data, quantitatively account for measures of stimulus-specific and homeostatic adaption in the primary visual cortex.