Statistical field theory captures collective non-equilibrium dynamics of neuronal networks , but it does not address the inverse problem of searching the connectivity to implement a desired dynamics. We here show for an analytically solvable network model that the effective action in statistical field theory is identical to the rate function in large deviation theory; using field theoretical methods we derive this rate function . It takes the form of a Kullback-Leibler divergence and enables data-driven inference of model parameters and Bayesian prediction of time series  .
We here unify the field theoretical approach to neuronal networks with large deviation 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 , Bayesian prediction of time series , and calculation of fluctuations beyond mean--field theory. Lastly, we expose a regime with fluctuation--induced transitions between mean--field solutions .
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Statistical field theory captures collective non-equilibrium dynamics of neuronal networks , but it does not address the inverse problem of searching the connectivity to implement a desired dynamics. We here show for an analytically solvable network model
We here unify the field theoretical approach to neuronal networks with large deviation theory. For a prototypical random recurrent network model with continuous-valued units, we show
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in large deviation theory; using field theoretical methods we derive this rate function . It
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, and calculation of fluctuations beyond mean--field theory. Lastly, we expose a regime with fluctuation--induced transitions between mean--field solutions