2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Collection 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Organizer(s) Ditlevsen, Susanne ; Faugeras, Olivier ; Galves, Antonio ; Reynaud-Bouret, Patricia ; Salort, Delphine ; Shinomoto, Shigeru

Date(s) 31/01/2022 - 04/02/2022

linked URL https://indico.math.cnrs.fr/event/6532/

00:00:00 / 00:00:00

4 30

Neural networks in the replica-mean field limits

By Thibault Taillefumier

In this talk, we propose to decipher the activity of neural networks via a “multiply and conquer” approach. This approach considers limit networks made of infinitely many replicas with the same basic neural structure. The key point is that these so-called replica-mean-field networks are in fact simplified, tractable versions of neural networks that retain important features of the finite network structure of interest. The finite size of neuronal populations and synaptic interactions is a core determinant of neural activity, being responsible for non-zero correlation in the spiking activity and for finite transition rates between metastable neural states. Mathematically, we develop our replica framework by expanding on ideas from the theory of communication networks to rigorously establish Poissonian mean-field limits for spiking networks. Computationally, we leverage this replica approach to characterize the stationary spiking activity of certain networks of the Galves Löcherbach type via reduction to tractable functional equations. We conclude by discussing perspectives about how to use our replica framework to probe nontrivial regimes of spiking correlations and transition rates between metastable neural states.

Information about the video

Date of recording 31/01/2022
Date of publication 31/01/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.004
Cite this video Taillefumier, Thibault (31/01/2022). Neural networks in the replica-mean field limits. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.004
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.004

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