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Probabilistic inference of binary Markov random fields in spiking neural networks through mean-field approximation

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posted on 2020-04-02, 11:21 authored by Yajing Zheng, Shanshan Jia, Zhaofei Yu, Tiejun Huang, Jian K Liu, Yonghong Tian
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in the brain. Previous studies have tried to relate the inference equation of binary Markov random fields to the dynamic equation of spiking neural networks through belief propagation algorithm and reparameterization, but they are valid only for Markov random fields with limited network structure. In this paper, we propose a spiking neural network model that can implement inference of arbitrary binary Markov random fields. Specifically, we design a spiking recurrent neural network and prove that its neuronal dynamics are mathematically equivalent to the inference process of Markov random fields by adopting mean-field theory. Furthermore, our mean-field approach unifies previous works. Theoretical analysis and experimental results, together with the application to image denoising, demonstrate that our proposed spiking neural network can get comparable results to that of mean-field inference.

Funding

This work is supported in part by the National Natural Science Foundation of China under grants 61806011, 61825101 and U1611461, in part by National Postdoctoral Program for Innovative Talents, China under grant BX20180005, in part by China Postdoctoral Science Foundation under grant 2018M630036, in part by the Zhejiang Lab, China under grants 2019KC0AB03 and 2019KC0AD02, in part by the Royal Society Newton Advanced Fellowship under grant NAF-R1-191082.

History

Citation

Neural Networks, 2020, Volume 126, pp. 42-51

Author affiliation

Department of Neuroscience, Psychology and Behaviour

Version

  • AM (Accepted Manuscript)

Published in

Neural Networks

Volume

126

Pagination

42-51

Publisher

Elsevier for 1. European Neural Network Society (ENNS) 2. International Neural Network Society (INNS) 3. Japanese Neural Network Society (JNNS)

issn

0893-6080

eissn

1879-2782

Acceptance date

2020-03-02

Copyright date

2020

Publisher version

https://www.sciencedirect.com/science/article/pii/S0893608020300800#d1e7412

Language

en

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