Data compression in sensory processing

Abstract

Along the early stages of many sensory pathways, significant downstream reductions occur in the numbers of neurons transmitting stimuli. To understand how much information is lost due to such a reduction, we investigate an idealized mathematical model of the retina using an integrate-and-fire type modeling structure. Our model features a large network of receptor cells randomly and sparsely coupled to a relatively small network of downstream neurons. Using numerical simulations of our model dynamical system and a static mean-field analytical reduction, we demonstrate firing patterns in the downstream neurons can in fact be used to reconstruct stimuli and confirm that mechanisms of data-preservation similar to compressive sensing may be at work in receptive fields. To address the underlying structure of our model and assess its biological realism, we study how the quality of the reconstruction depends on our choice of physiological features, reflected by the model parameters. Moreover, we extend our idealized model to address a number of more realistic scenarios, including clumped receptive fields and temporally varying stimuli. Our methods are expected to provide guidance for studying information loss in more realistic neuronal network models as well as experiments investigating stimuli reconstruction in sensory pathways.