Journal Article

FZJ-2021-02726

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Transient Chaotic Dimensionality Expansion by Recurrent Networks

Keup, C. (Corresponding author)FZJ* ; Kühn, T. ; Dahmen, D.FZJ* ; Helias, M. (Last author)FZJ*

2021
APS College Park, Md.

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Please use a persistent id in citations: http://hdl.handle.net/2128/28437  doi:10.1103/PhysRevX.11.021064

Abstract: 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.

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Contributing Institute(s):

1. Computational and Systems Neuroscience (INM-6)
2. Theoretical Neuroscience (IAS-6)
3. Jara-Institut Brain structure-function relationships (INM-10)

Research Program(s):

1. 5232 - Computational Principles (POF4-523) (POF4-523)
2. 5231 - Neuroscientific Foundations (POF4-523) (POF4-523)
3. MSNN - Theory of multi-scale neuronal networks (HGF-SMHB-2014-2018) (HGF-SMHB-2014-2018)
4. GRK 2416 - GRK 2416: MultiSenses-MultiScales: Neue Ansätze zur Aufklärung neuronaler multisensorischer Integration (368482240) (368482240)
5. neuroIC002 - Recurrence and stochasticity for neuro-inspired computation (EXS-SF-neuroIC002) (EXS-SF-neuroIC002)
6. SDS005 - Towards an integrated data science of complex natural systems (PF-JARA-SDS005) (PF-JARA-SDS005)

Appears in the scientific report 2021

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