Efficient, simulation-free estimators of firing rates with Markovian surrogates

TL;DR

This paper introduces efficient, simulation-free estimators for neural firing rates using Markovian surrogates, significantly simplifying the analysis of complex spiking neural networks.

Contribution

It presents a novel hierarchy of Markovian approximations that enable accurate firing rate estimation without simulations, incorporating spiking synchrony for improved precision.

Findings

Markovian surrogates effectively estimate firing rates

Spiking synchrony enhances estimator accuracy

Method simplifies analysis of complex neural models

Abstract

Spiking neural networks (SNNs) are powerful mathematical models that integrate the biological details of neural systems, but their complexity often makes them computationally expensive and analytically untractable. The firing rate of an SNN is a crucial first-order statistic to characterize network activity. However, estimating firing rates analytically from even simplified SNN models is challenging due to 1) the intricate dependence between the nonlinear network dynamics and parameters, and 2) the singularity and irreversibility of spikes. In this Letter, we propose a class of computationally efficient, simulation-free estimators of firing rates. This is based on a hierarchy of Markovian approximations that reduces the complexity of SNN dynamics. We show that while considering firing rates alone is insufficient for accurate estimations of themselves, the information of spiking synchrony dramatically improves the estimator's accuracy. This approach provides a practical tool for brain modelers, directly mapping biological parameters to firing rate.