Mesoscopic modeling of hidden spiking neurons

Shuqi Wang, Valentin Schmutz, Guillaume Bellec, Wulfram Gerstner

Keywords: recurrent spiking neural network, hidden spiking neurons, maximum likelihood, mean-field approximation, finite-size fluctuations, neural population dynamics, latent variable model, expectation-maximization algorithm, metastable dynamics

TL;DR: We derive a neuronally-grounded latent variable model for multi-neuronal spike trains.

Abstract: Can we use spiking neural networks (SNN) as generative models of multi-neuronal recordings, while taking into account that most neurons are unobserved? Modeling the unobserved neurons with large pools of hidden spiking neurons leads to severely underconstrained problems that are hard to tackle with maximum likelihood estimation. In this work, we use coarse-graining and mean-field approximations to derive a bottom-up, neuronally-grounded latent variable model (neuLVM), where the activity of the unobserved neurons is reduced to a low-dimensional mesoscopic description. In contrast to previous latent variable models, neuLVM can be explicitly mapped to a recurrent, multi-population SNN, giving it a transparent biological interpretation. We show, on synthetic spike trains, that a few observed neurons are sufficient for neuLVM to perform efficient model inversion of large SNNs, in the sense that it can recover connectivity parameters, infer single-trial latent population activity, reproduce ongoing metastable dynamics, and generalize when subjected to perturbations mimicking optogenetic stimulation.

Community Implementations: [ 3 code implementations](https://www.catalyzex.com/paper/arxiv:2205.13493/code)