Published in Computational and Systems Neuroscience (CoSyNe), (II-1), Feb 2012.
Efficient coding provides a powerful principle for explaining early sensory processing. Most attempts to test this principle have been limited to linear, noiseless models, and when applied to natural images, have yielded localized oriented filters (e.g., Bell and Sejnowski, 1995). Although this is generally consistent with cortical representations, it fails to account for basic properties of early vision, such as the receptive field organization, temporal dynamics, and nonlinear behaviors in retinal ganglion cells (RGCs). Here we show that an efficient coding model that incorporates ingredients critical to biological computation -- input and output noise, nonlinear response functions, and a metabolic cost on the firing rate -- can predict several basic properties of retinal processing. Specifically, we develop numerical methods for simultaneously optimizing linear filters and response nonlinearities of a population of model neurons so as to maximize information transmission in the presence of noise and metabolic costs. We place no restrictions on the form of the linear filters, and assume only that the nonlinearities are monotonically increasing.
In the case of vanishing noise, our method reduces to a generalized version of independent component analysis; training on natural image patches produces localized oriented filters and smooth nonlinearities. When the model includes biologically realistic levels of noise, the predicted filters are center-surround and the nonlinearities are rectifying, consistent with properties of RGCs. The model yields two populations of neurons, with On- and Off-center responses, which independently tile the visual space. As observed in the primate retina, Off-center neurons are more numerous and have filters with smaller spatial extent. Applied to natural movies, the model yields filters that are approximately space-time separable, with a center-surround spatial profile, a biphasic temporal profile, and a surround response that is slightly delayed relative to the center, consistent with retinal processing.