Large deviations, dynamics and phase transitions in large stochastic and disordered neural networks

DOI10.1007/s10955-013-0818-5zbMath1291.82099arXiv1302.6951OpenAlexW2257652304WikidataQ105583419 ScholiaQ105583419MaRDI QIDQ2016499

Tanguy Cabana, Jonathan D. Touboul

Publication date: 20 June 2014

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6951

zbMATH Keywords

phase transitionslarge deviationsmean-field equationsheterogeneous neuronal networks

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Phase transitions (general) in equilibrium statistical mechanics (82B26) Neural nets applied to problems in time-dependent statistical mechanics (82C32) Transition functions, generators and resolvents (60J35)

Related Items (10)

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays ⋮ Interacting diffusions on sparse graphs: hydrodynamics from local weak limits ⋮ Symmetries constrain dynamics in a family of balanced neural networks ⋮ An emergent autonomous flow for mean-field spin glasses ⋮ Mathematical studies of the dynamics of finite-size binary neural networks: a review of recent progress ⋮ Large deviations for randomly connected neural networks: I. Spatially extended systems ⋮ Large deviations for randomly connected neural networks: II. State-dependent interactions ⋮ Universality for Langevin-like spin glass dynamics ⋮ Interacting diffusions on random graphs with diverging average degrees: hydrodynamics and large deviations ⋮ Large Population Asymptotics for Interacting Diffusions in a Quenched Random Environment

Cites Work

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• Mean-field equations for stochastic firing-rate neural fields with delays: derivation and noise-induced transitions
• Large deviations for some weakly dependent random processes
• Large deviations techniques and applications.
• Introduction to functional differential equations
• Mean-field equations, bifurcation map and route to chaos in discrete time neural networks
• Averaged and quenched propagation of chaos for spin glass dynamics
• Large deviations and mean-field theory for asymmetric random recurrent neural networks
• Large deviations for Langevin spin glass dynamics
• Propagation of chaos in neural fields
• Spatiotemporal dynamics of continuum neural fields
• [https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
• Stochastic Equations in Infinite Dimensions
• Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
• Systematic Fluctuation Expansion for Neural Network Activity Equations
• Neural networks and physical systems with emergent collective computational abilities.
• Noise-Induced Behaviors in Neural Mean Field Dynamics
• Characteristics of Random Nets of Analog Neuron-Like Elements
• Prescribing a System of Random Variables by Conditional Distributions
• Mean-field theory and synchronization in random recurrent neural networks

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