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Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons.

Buesing, L; Bill, J; Nessler, B; Maass, W; (2011) Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons. PLoS Computational Biology , 7 (11) , Article e1002211. 10.1371/journal.pcbi.1002211. Green open access

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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.

Type: Article
Title: Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons.
Location: US
Open access status: An open access version is available from UCL Discovery
DOI: 10.1371/journal.pcbi.1002211
Publisher version: http://dx.doi.org/10.1371/journal.pcbi.1002211
Language: English
Additional information: © 2011 Buesing et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. PMCID: PMC3207943
Keywords: Action Potentials, Algorithms, Animals, Computer Simulation, Humans, Markov Chains, Models, Neurological, Monte Carlo Method, Neurons, Primates, Stochastic Processes
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Life Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1365537
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