A simple model of optimal population coding for sensory systems

A fundamental task of a sensory system is to infer information about the environment. It has long been suggested that an important goal of the first stage of this process is to encode the raw sensory signal efficiently by reducing its redundancy in the neural representation. Some redundancy, however, would be expected because it can provide robustness to noise inherent in the system. Encoding the raw sensory signal itself is also problematic, because it contains distortion and noise. The optimal solution would be constrained further by limited biological resources. Here, we analyze a simple theoretical model that incorporates these key aspects of sensory coding, and apply it to conditions in the retina. The model specifies the optimal way to incorporate redundancy in a population of noisy neurons, while also optimally compensating for sensory distortion and noise. Importantly, it allows an arbitrary input-to-output cell ratio between sensory units (photoreceptors) and encoding units (retinal ganglion cells), providing predictions of retinal codes at different eccentricities. Compared to earlier models based on redundancy reduction, the proposed model conveys more information about the original signal. Interestingly, redundancy reduction can be near-optimal when the number of encoding units is limited, such as in the peripheral retina. We show that there exist multiple, equally-optimal solutions whose receptive field structure and organization vary significantly. Among these, the one which maximizes the spatial locality of the computation, but not the sparsity of either synaptic weights or neural responses, is consistent with known basic properties of retinal receptive fields. The model further predicts that receptive field structure changes less with light adaptation at higher input-to-output cell ratios, such as in the periphery.
Author Summary Studies of the computational principles of sensory coding have largely focused on the redundancy reduction hypothesis, which posits that a neural population should encode the raw sensory signal efficiently by reducing its redundancy. Models based on this idea, however, have not taken into account some important aspects of sensory systems. First, neurons are noisy, and therefore, some redundancy in the code can be useful for transmitting information reliably. Second, the sensory signal itself is noisy, which should be counteracted as early as possible in the sensory pathway. Finally, neural resources such as the number of neurons are limited, which should strongly affect the form of the sensory code. Here we examine a simple model that takes all these factors into account. We find that the model conveys more information compared to redundancy reduction. When applied to the retina, the model provides a unified functional account for several known properties of retinal coding and makes novel predictions that have yet to be tested experimentally. The generality of the framework allows it to model a wide range of conditions and can be applied to predict optimal sensory coding in other systems.