Workshop on Methods of Information Theory in Computational NeuroscienceJesus MaloUniversitat de Valencia
Information flow under visual cortical magnification: Gaussianization estimates and theoretical results
Computations done by individual neural layers along the visual pathway (e.g. opponency at chromatic channels and their saturation, spatial filtering and the nonlinearities of the texture sensors at visual cortex) have been suggested to be organized for optimal information transmission. However, the efficiency of these layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint array of spatio-chromatic responses.
In this work we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted through a network based on a recent Gaussianization technique. Our Gaussianization reduces the challenging multivariate density estimation problem to a set of simpler univariate estimations. Here we extend our previous results [Gomez et al. J.Neurophysiol.2020, arxiv:1907.13046] and [J.Malo arxiv:1910.01559] to address the problem posed by cortical magnification. Cortical magnification implies an expansion of the dimensionality of the signal, and here the proposed total correlation estimator is compared to theoretical predictions that work in scenarios that do not preserve the dimensionality.
In psychophysically tuned networks with Poisson noise, and assuming sensors of equivalent signal/noise quality at different neural layers, results on transmitted information show that: (1) progressively deeper representations are better in terms of the amount of information captured about the input, (2) the transmitted information up to the cortical representation follows the PDF of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially bigger than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.
A. Gomez-Villa, M. Bertalmio and J. Malo (2020). Visual information flow in Wilson–Cowan networks. J. Neurophysiology.
J. Malo (2020). Spatio-Chromatic Information available from different Neural Layers via Gaussianization.
