The Distribution of Unstable Fixed Points in Chaotic Neural Networks
Jakob Stubenrauch, Christian Keup, Anno Christopher Kurth, Moritz Helias, Alexander van Meegen · arXiv (Cornell University) · 2022
We analytically determine the number and distribution of fixed points in a canonical model of a chaotic neural network. This distribution reveals that fixed points and dynamics are confined to separate shells in phase space. Furthermore, the distribution enables us to determine the eigenvalue spectra of the Jacobian at the fixed points. Despite the radial separation of fixed points and dynamics, we find that nearby fixed points act as partially attracting landmarks for the dynamics.