Autonomous learning of nonlocal stochastic neuron dynamics

TL;DR

This paper introduces two novel closure methods for nonlocal stochastic neuron models driven by correlated noise, enabling better analysis of neuronal information processing and dynamics.

Contribution

It proposes a modified nonlocal large-eddy-diffusivity closure and a data-driven closure using sparse regression for stochastic neuron equations.

Findings

The closures accurately model neuron dynamics under colored noise.

Mutual information between stimulus and neuron states is effectively computed.

Methods are validated on leaky integrate-and-fire and FitzHugh-Nagumo neurons.

Abstract

Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions, which is (partially) characterized by the single-time joint probability density function (PDF) of system states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for the stochastic non-spiking leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.