Transient Chaotic Dimensionality Expansion by Recurrent Networks

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these two forms of signaling? We develop a unified mean-field the...

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Autores principales:	Christian Keup, Tobias Kühn, David Dahmen, Moritz Helias
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/d9b148f6487e4d21b90cabda7eb6ce92
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spelling	oai:doaj.org-article:d9b148f6487e4d21b90cabda7eb6ce922021-12-02T17:13:20ZTransient Chaotic Dimensionality Expansion by Recurrent Networks10.1103/PhysRevX.11.0210642160-3308https://doaj.org/article/d9b148f6487e4d21b90cabda7eb6ce922021-06-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021064http://doi.org/10.1103/PhysRevX.11.021064https://doaj.org/toc/2160-3308Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these two forms of signaling? We develop a unified mean-field theory for large random networks to show that first- and second-order statistics in rate and binary networks are in fact identical if rate neurons receive the right amount of noise. Their response to presented stimuli, however, can be radically different. We quantify these differences by studying how nearby state trajectories evolve over time, asking to what extent the dynamics is chaotic. Chaos in the two models is found to be qualitatively different. In binary networks, we find a network-size-dependent transition to chaos and a chaotic submanifold whose dimensionality expands stereotypically with time, while rate networks with matched statistics are nonchaotic. Dimensionality expansion in chaotic binary networks aids classification in reservoir computing and optimal performance is reached within about a single activation per neuron; a fast mechanism for computation that we demonstrate also in spiking networks. A generalization of this mechanism extends to rate networks in their respective chaotic regimes.Christian KeupTobias KühnDavid DahmenMoritz HeliasAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021064 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Christian Keup Tobias Kühn David Dahmen Moritz Helias Transient Chaotic Dimensionality Expansion by Recurrent Networks
description	Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these two forms of signaling? We develop a unified mean-field theory for large random networks to show that first- and second-order statistics in rate and binary networks are in fact identical if rate neurons receive the right amount of noise. Their response to presented stimuli, however, can be radically different. We quantify these differences by studying how nearby state trajectories evolve over time, asking to what extent the dynamics is chaotic. Chaos in the two models is found to be qualitatively different. In binary networks, we find a network-size-dependent transition to chaos and a chaotic submanifold whose dimensionality expands stereotypically with time, while rate networks with matched statistics are nonchaotic. Dimensionality expansion in chaotic binary networks aids classification in reservoir computing and optimal performance is reached within about a single activation per neuron; a fast mechanism for computation that we demonstrate also in spiking networks. A generalization of this mechanism extends to rate networks in their respective chaotic regimes.
format	article
author	Christian Keup Tobias Kühn David Dahmen Moritz Helias
author_facet	Christian Keup Tobias Kühn David Dahmen Moritz Helias
author_sort	Christian Keup
title	Transient Chaotic Dimensionality Expansion by Recurrent Networks
title_short	Transient Chaotic Dimensionality Expansion by Recurrent Networks
title_full	Transient Chaotic Dimensionality Expansion by Recurrent Networks
title_fullStr	Transient Chaotic Dimensionality Expansion by Recurrent Networks
title_full_unstemmed	Transient Chaotic Dimensionality Expansion by Recurrent Networks
title_sort	transient chaotic dimensionality expansion by recurrent networks
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/d9b148f6487e4d21b90cabda7eb6ce92
work_keys_str_mv	AT christiankeup transientchaoticdimensionalityexpansionbyrecurrentnetworks AT tobiaskuhn transientchaoticdimensionalityexpansionbyrecurrentnetworks AT daviddahmen transientchaoticdimensionalityexpansionbyrecurrentnetworks AT moritzhelias transientchaoticdimensionalityexpansionbyrecurrentnetworks
_version_	1718381349865259008

Transient Chaotic Dimensionality Expansion by Recurrent Networks

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