# Biological direct-shortcut deep residual learning for sparse visual processing

## TL;DR

The paper suggests that the primary visual cortex functions like a deep residual neural network optimized for sparse image processing.

## Contribution

The paper proposes that the primary visual cortex operates as a biological ResNet with sparse representations and direct shortcuts.

## Key findings

- Gabor-like basis functions in V1 are effective for sparse natural image representation.
- Intra-layer synaptic weight matrices in V1 can be approximated by sparse identity mappings.
- The structure of V1 resembles direct-shortcut ResNets, linking sparse image representation to sparse intra-layer weights.

## Abstract

We show, based on the following three grounds, that the primary visual cortex (V1) is a biological direct-shortcut deep residual learning neural network (ResNet) for sparse visual processing: (1) We first highlight that Gabor-like sets of basis functions, which are similar to the receptive fields of simple cells in the primary visual cortex (V1), are excellent candidates for sparse representation of natural images; i.e., images from the natural world, affirming the brain to be optimized for this. (2) We then prove that the intra-layer synaptic weight matrices of this region can be reasonably first-order approximated by identity mappings, and are thus sparse themselves. (3) Finally, we point out that intra-layer weight matrices having identity mapping as their initial approximation, irrespective of this approximation being also a reasonable first-order one or not, resemble the building blocks of direct-shortcut digital ResNets, which completes the grounds. This biological ResNet interconnects the sparsity of the final representation of the image to that of its intra-layer weights. Further exploration of this ResNet, and understanding the joint effects of its architecture and learning rules, e.g. on its inductive bias, could lead to major advancements in the area of bio-inspired digital ResNets. One immediate line of research in this context, for instance, is to study the impact of forcing the direct-shortcuts to be good first-order approximations of each building block. For this, along with the \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${{\ell}}_{1}$$\end{document}ℓ1-minimization posed on the basis function coefficients the ResNet finally provides at its output, another parallel one could e.g. also be posed on the weights of its residual layers.