Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

TLDR

The organization of computations in spiking‑neuron networks remains largely unknown, despite the existence of a powerful stochastic inference framework based on sampling that explains many macroscopic neural phenomena, yet linking these abstract models to detailed spiking dynamics has proven surprisingly difficult. This study establishes a link by showing that, under certain conditions, the stochastic firing of spiking‑neuron networks can be interpreted as probabilistic inference via Markov chain Monte Carlo sampling. To achieve this, the authors introduce a non‑reversible Markov chain approach compatible with spiking dynamics, propose a neural network model, and provide rigorous analysis demonstrating that its activity implements MCMC sampling in both discrete and continuous time. The results confirm that spiking‑neuron activity can perform MCMC sampling, thereby narrowing the gap between abstract cortical computation models and detailed neuronal network dynamics.

Abstract

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.