[Paper Review] Visual Information flow in Wilson-Cowan networks

Alexander Gómez-Villa, Marcelo Bertalmı́o+1 more|PubMed|Jul 30, 2019

Visual perception and processing mechanisms67 references4 citations

TL;DR

This paper analyzes the communication efficiency of a psychophysically-tuned Wilson-Cowan network modeling the retina-V1 pathway using multivariate total correlation. It shows that despite no explicit optimization for independence, the network significantly reduces redundancy—especially through nonlinear local contrast and oriented filtering—confirming its alignment with the Efficient Coding Hypothesis and suggesting utility in image compression.

ABSTRACT

In this paper, we study the communication efficiency of a psychophysically tuned cascade of Wilson-Cowan and divisive normalization layers that simulate the retina-V1 pathway. This is the first analysis of Wilson-Cowan networks in terms of multivariate total correlation. The parameters of the cortical model have been derived through the relation between the steady state of the Wilson-Cowan model and the divisive normalization model. The communication efficiency has been analyzed in two ways: First, we provide an analytical expression for the reduction of the total correlation among the responses of a V1-like population after the application of the Wilson-Cowan interaction. Second, we empirically study the efficiency with visual stimuli and statistical tools that were not available before <i>1</i>) we use a recent, radiometrically calibrated, set of natural scenes, and <i>2</i>) we use a recent technique to estimate the multivariate total correlation in bits from sets of visual responses, which only involves univariate operations, thus giving better estimates of the redundancy. The theoretical and the empirical results show that, although this cascade of layers was not optimized for statistical independence in any way, the redundancy between the responses gets substantially reduced along the neural pathway. Specifically, we show that <i>1</i>) the efficiency of a Wilson-Cowan network is similar to its equivalent divisive normalization model; <i>2</i>) while initial layers (Von Kries adaptation and Weber-like brightness) contribute to univariate equalization, and the bigger contributions to the reduction in total correlation come from the computation of nonlinear local contrast and the application of local oriented filters; and <i>3</i>) psychophysically tuned models are more efficient (reduce more total correlation) in the more populated regions of the luminance-contrast plane. These results are an alternative confirmation of the efficient coding hypothesis for the Wilson-Cowan systems, and, from an applied perspective, they suggest that neural field models could be an option in image coding to perform image compression.<b>NEW & NOTEWORTHY</b> The Wilson-Cowan interaction is analyzed in total correlation terms for the first time. Theoretical and empirical results show that this psychophysically tuned interaction achieves the biggest efficiency in the most frequent region of the image space. This is an original confirmation of the efficient coding hypothesis and suggests that neural field models can be an alternative to divisive normalization in image compression.

Motivation & Objective

• To analyze the communication efficiency of Wilson-Cowan networks in terms of multivariate total correlation, a measure of redundancy in neural population responses.
• To evaluate whether psychophysically-tuned Wilson-Cowan models reduce redundancy along the retina-V1 pathway, as predicted by the Efficient Coding Hypothesis.
• To compare the redundancy reduction performance of Wilson-Cowan networks with their equivalent Divisive Normalization counterparts.
• To assess the contribution of individual processing stages (e.g., contrast, orientation filtering) to total correlation reduction using accurate statistical estimation.
• To explore the potential of neural field models for image compression by quantifying their information-theoretic efficiency.

Proposed method

• The study employs a cascade of four isomorphic linear+nonlinear modules modeling the retina-V1 pathway, with the final nonlinearity replaced by an equivalent Wilson-Cowan model.
• The Wilson-Cowan dynamics are defined by a system of differential equations with parameters derived from the steady-state equivalence to Divisive Normalization, including auto-attenuation (α), interaction matrix (W), and saturation function (f(x) = c·x^γ).
• A radiometrically calibrated database of natural scenes is used as input stimuli to ensure realistic visual input for response analysis.
• A recent multivariate Gaussianization technique is applied to estimate total correlation in bits from neural responses using only univariate operations, enabling accurate redundancy measurement without multivariate density estimation.
• The Jacobian of the transformation is computed to model local signal deformation, crucial for information-theoretic analysis of redundancy.
• Theoretical analysis derives an analytical expression for total correlation reduction after Wilson-Cowan transformation, validated empirically with natural image stimuli.

Experimental results

Research questions

• RQ1 To what extent does a Wilson-Cowan network reduce multivariate total correlation in neural population responses along the retina-V1 pathway?
• RQ2 How does the redundancy reduction performance of the Wilson-Cowan model compare to its equivalent Divisive Normalization model?
• RQ3 Which processing stages (e.g., Von-Kries, contrast, orientation) contribute most to total correlation reduction?
• RQ4 Are psychophysically-tuned models more efficient in reducing redundancy across different regions of the luminance-contrast plane?
• RQ5 Can neural field models like Wilson-Cowan be effective for image compression based on their information-theoretic efficiency?

Key findings

• The Wilson-Cowan network reduces total correlation substantially along the neural pathway, even without explicit optimization for statistical independence.
• The communication efficiency of the Wilson-Cowan model is comparable to that of its equivalent Divisive Normalization model in terms of redundancy reduction.
• Nonlinear local contrast computation and local oriented filtering contribute more significantly to redundancy reduction than univariate equalization stages like Von-Kries adaptation.
• Psychophysically-tuned models reduce more total correlation in the more populated regions of the luminance-contrast plane, indicating higher efficiency under natural stimulus statistics.
• The use of a multivariate Gaussianization-based estimator enables accurate, univariate-based estimation of total correlation, overcoming prior limitations in multivariate density estimation.
• The results provide strong support for the Efficient Coding Hypothesis in the context of Wilson-Cowan neural field models, suggesting their potential in bio-inspired image compression.