Design principles for cost functions in optimal sensory coding

Studies of neural codes for sensory variables are rooted in the long-established principle that neural codes are organized to encode as much information as possible about sensory stimuli. This principle has been successful in explaining many features of neural activity, suggesting that a key component of a cost function determining sensory neural coding from first principles is the stimulus encoding error. However, recent work has shown that neural cost functions may have other terms reflecting costs or limitations of the biological hardware. One key piece is the metabolic cost of neural activity. Including metabolic cost in the cost function leads to optimized spiking models that exhibit spike-triggered adaptation. Another possible component of the neural cost function is reliable downstream transmission of information. Neurons have short integration time constants, which make it difficult for information to be transmitted reliably unless inputs to neurons are correlated. This suggests that cost functions accounting for constraints on downstream readout promote codes with redundancy-inducing correlations. We review and discuss evidence that neural codes in the brain have features consistent with the predictions expected if cost functions have additional terms beyond the encoding error. Adaptation currents are indeed present in biological neurons with the time scales predicted by metabolically efficient codes, and neural population codes have information-reducing correlations that support downstream information transmission. Finally, we discuss future directions important for fully establishing the different contributions to neural cost functions.