The Distribution of Unstable Fixed Points in Chaotic Neural Networks
Abstract
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.
Keywords
Cite
@article{arxiv.2210.07877,
title = {The Distribution of Unstable Fixed Points in Chaotic Neural Networks},
author = {Jakob Stubenrauch and Christian Keup and Anno C. Kurth and Moritz Helias and Alexander van Meegen},
journal= {arXiv preprint arXiv:2210.07877},
year = {2023}
}
Comments
37 pages, 11 figures. Main changes include: - additional analysis of the fixed points' role for the dynamics - replica calculation for the random determinant (removing a previous assumption) - extensive investigation of finite size effects - asymptotic results for the number of fixed points and their distribution at the edge of chaos and in the strongly chaotic limit