Efficient coding explains neural response homeostasis and stimulus-specific adaptation

Neurons are typically sensitive to a small fraction of possible stimuli in sensory space. If the environment changes, making certain stimuli more prevalent, neurons sensitive to those stimuli respond more often and therefore have a higher average firing rate. Prolonged exposure to such an environment often causes such neurons to adapt by responding less vigorously. If adaptation consistently returns the average firing rate to its value prior to environmental shift, it is termed firing-rate homeostasis. We present a normative explanation of firing-rate homeostasis grounded in the Infomax principle. Homeostasis arises as the optimal solution to a trade-off between coding fidelity and metabolic cost, understood as the average population spike count. Our framework gives quantitative conditions necessary for the optimality of homeostasis, and predicts how adaptation should deviate from homeostasis when these conditions are violated. Based on biological estimates of relevant parameters, we show that these conditions hold in areas of cortex where homeostatic adaptation has been observed. Another feature of adaptation within sensory cortex is stimulus specific adaptation, under which neurons not only change their responsiveness, but also the shape of their tuning curves. This often takes the form of repulsion of preferred stimuli away from an adaptor stimulus. We demonstrate how homeostatic coding, coupled with Bayesian theories of neural representation, can explain such stimulus-specific adaptation effects (e.g., in V1), which we show can be implemented by divisive normalisation with adaptive weights. Furthermore, our framework gives a computational interpretation to the feedforward inputs and weights of the divisive normalisation operation. In summary, we show analytically that homeostasis is the optimal solution to maximising the informational content of population responses with limited energetic resources, irrespective of the computations encoded by the population.