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

20 30

Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models

By Michel Davydov

In order to model neural computations resulting from myriads of neuronal interactions, intensity-based spiking neural networks are commonly used. Unfortunately, most relevant dynamics involve complex graphs of interactions for which an exact computational treatment is impossible. To circumvent this difficulty, the replica-mean-field approach focuses on randomly interacting replicas of the networks of interest. In contrast with classical thermodynamic mean-fields, interaction couplings do not scale with the number of neurons and preserve both the geometry of the network and the finite-size correlations. In the limit of an infinite number of replicas, these networks become analytically tractable under the so-called Poisson Hypothesis, which postulates that replicas become asymptotically independent and arrivals to a given neuron become Poisson distributed. This hypothesis is often conjectured or numerically validated but not proven. We show the validity of the Poisson Hypothesis for large classes of processes that include for example Galves-Löcherbach models.

Information about the video

Date of recording 03/02/2022
Date of publication 03/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.020
Cite this video Davydov, Michel (03/02/2022). Propagation of Chaos and Poisson Hypothesis for Replica Mean-Field Models. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.020
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.020

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