Information Geometry of the Retinal Representation Manifold

Abstract

The ability to discriminate visual stimuli is constrained by their retinal representations. Previous studies of visual discriminability were limited to either low-dimensional artificial stimuli or theoretical considerations without a realistic model. Here we propose a novel framework for understanding stimulus discriminability achieved by retinal representations of naturalistic stimuli with the method of information geometry. To model the joint probability distribution of neural responses conditioned on the stimulus, we created a stochastic encoding model of a population of salamander retinal ganglion cells based on a three-layer convolutional neural network model. This model not only accurately captured the mean response to natural scenes but also a variety of second-order statistics. With the model and the proposed theory, we are able to compute the Fisher information metric over stimuli and study the most discriminable stimulus directions. We found that the most discriminable stimulus varied substantially, allowing an examination of the relationship between the most discriminable stimulus and the current stimulus. We found that the most discriminative response mode is often aligned with the most stochastic mode. This finding carries the important implication that under natural scenes noise correlations in the retina are information-limiting rather than aiding in increasing information transmission as has been previously speculated. We observed that sensitivity saturates less in the population than for single cells and also that Fisher information varies less than sensitivity as a function of firing rate. We conclude that under natural scenes, population coding benefits from complementary coding and helps to equalize the information carried by different firing rates, which may facilitate decoding of the stimulus under principles of information maximization.