Consiglio Nazionale delle Ricerche

Tipo di prodottoArticolo in rivista
TitoloPath integral approach to random neural networks
Anno di pubblicazione2018
Formato-
Autore/iCrisanti, A.; Sompolinksy, H.
Affiliazioni autoriDepartment of Physiscs, Institute of Complex Systems (ISC-CNR), University la Sapienza, P.le Aldo Moro 2, Rome, I-00185, Italy Racah Institute of Physics, Edmond and Lily Safra Center for Brain Sciences, Hebrew University of Jerusalem, 9190401, Israel
Autori CNR e affiliazioni
  • ANDREA CRISANTI
Lingua/e
  • inglese
AbstractIn this work we study of the dynamics of large-size random neural networks. Different methods have been developed to analyze their behavior, and most of them rely on heuristic methods based on Gaussian assumptions regarding the fluctuations in the limit of infinite sizes. These approaches, however, do not justify the underlying assumptions systematically. Furthermore, they are incapable of deriving in general the stability of the derived mean-field equations, and they are not amenable to analysis of finite-size corrections. Here we present a systematic method based on path integrals which overcomes these limitations. We apply the method to a large nonlinear rate-based neural network with random asymmetric connectivity matrix. We derive the dynamic mean field (DMF) equations for the system and the Lyapunov exponent of the system. Although the main results are well known, here we present the detailed calculation of the spectrum of fluctuations around the mean-field equations from which we derive the general stability conditions for the DMF states. The methods presented here can be applied to neural networks with more complex dynamics and architectures. In addition, the theory can be used to compute systematic finite-size corrections to the mean-field equations.
Lingua abstractinglese
Altro abstract-
Lingua altro abstract-
Pagine da062120-1
Pagine a062120-16
Pagine totali16
RivistaPhysical review. E (Print)
Attiva dal 2016
Editore: American Physical Society - Ridge, NY
Paese di pubblicazione: Stati Uniti d'America
Lingua: inglese
ISSN: 2470-0045
Titolo chiave: Physical review. E (Print)
Titolo proprio: Physical review
Titolo abbreviato: Phys Rev E
Titolo alternativo: PRE
Numero volume della rivista98
Fascicolo della rivista6
DOI10.1103/PhysRevE.98.062120
Verificato da referee-
Stato della pubblicazionePublished version
Indicizzazione (in banche dati controllate)
  • ISI Web of Science (WOS) (Codice:000452954300001)
Parole chiaveLyapunov methods, Quantum theory, onnectivity matrix, Finite-size corrections, Gaussian assumption, General stabilities, Mean field equation
Link (URL, URI)https://journals.aps.org/pre/pdf/10.1103/PhysRevE.98.062120
Titolo parallelo-
Licenza-
Scadenza embargo-
Data di accettazione-
Note/Altre informazioni-
Strutture CNR
  • ISC — Istituto dei sistemi complessi
Moduli/Attività/Sottoprogetti CNR-
Progetti Europei-
Allegati
Path integral approach to random neural networks (documento privato )
Tipo documento: application/pdf