Phase Space Analysis of Chaotic Neural Networks

Autor:	Stubenrauch, Jakob, Keup, Christian, Kurth, Anno C., Helias, Moritz, van Meegen, Alexander
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	FOS: Physical sciences Physical sciences [FOS] Disordered Systems and Neural Networks (cond-mat.dis-nn) Chaotic Dynamics (nlin.CD) Condensed Matter - Disordered Systems and Neural Networks Nonlinear Sciences - Chaotic Dynamics
Zdroj:	arXiv (2022). doi:10.48550/ARXIV.2210.07877
DOI:	10.48550/ARXIV.2210.07877
Popis:	We analytically determine the 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. Perhaps counter-intuitively, the velocity of the dynamics is strongly correlated with the direction imposed by the nearest fixed point despite the spatial separation. We propose that this influence of the fixed points is mediated by tangentially fixed lines. 26 pages, 8 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::074d5cd9b774fbf3d4693320a2a91a94 http://arxiv.org/abs/2210.07877 Zobrazit plný text záznamu