Large Deviations Approach to Random Recurrent Neuronal Networks: Parameter Inference and Fluctuation-Induced Transitions

Abstract

We here unify the field theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate function and derive the latter using field theory. This rate function takes the form of a Kullback-Leibler divergence which enables data-driven inference of model parameters and calculation of fluctuations beyond mean-field theory. Lastly, we expose a regime with fluctuation-induced transitions between mean-field solutions.

Extension to multiple populations

References in corpus (4)

• The large deviation approach to statistical mechanics
• Transition to chaos in random networks with cell-type-specific connectivity
• Dynamics of Random Neural Networks with Bistable Units
• Transient chaotic dimensionality expansion by recurrent networks

Cited by in corpus (6)

• Dimension of activity in random neural networks
• Does the brain behave like a (complex) network? I. Dynamics
• Unified field theoretical approach to deep and recurrent neuronal networks
• Extended Anderson Criticality in Heavy-Tailed Neural Networks
• Lagrangian stochastic integrals of motion in isotropic random flows
• Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics