Neural networks as set-valued dynamical systems and the universality of the windowed Fourier transform

Abstract

The visual pathway and other brain structures consist of a large number of layers of neurons. At each point of a three-dimensional laminated structure there exists a direction\(\hat n\) that is perpendicular to the layers. Assuming an information flow from top to bottom, the perceptive field of the neurons grows as one moves in the direction\(\hat n\). This enables the system to perform a multiscale analysis.