Perturbation theory for stochastic learning dynamics

Todd K. Leen; Robert Friel

doi:10.1109/IJCNN.2011.6033476

Perturbation theory for stochastic learning dynamics

Todd K. Leen, Robert Friel

Biomedical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

On-line machine learning and biological spike-timing-dependent plasticity (STDP) rules both generate Markov chains for the synaptic weights. We give a perturbation expansion (in powers of the learning rate) for the dynamics that, unlike the usual approximation by a Fokker-Planck equation (FPE), is rigorous. Our approach extends the related system size expansion by giving an expansion for the probability density as well as its moments. Applied to two observed STDP learning rules, our approach provides better agreement with Monte-Carlo simulations than either the FPE or a simple linearized theory. The approach is also applicable to stochastic neural dynamics.

Original language	English (US)
Title of host publication	2011 International Joint Conference on Neural Networks, IJCNN 2011 - Final Program
Pages	2031-2038
Number of pages	8
DOIs	https://doi.org/10.1109/IJCNN.2011.6033476
State	Published - 2011
Event	2011 International Joint Conference on Neural Network, IJCNN 2011 - San Jose, CA, United States Duration: Jul 31 2011 → Aug 5 2011

Publication series

Name	Proceedings of the International Joint Conference on Neural Networks

Other

Other	2011 International Joint Conference on Neural Network, IJCNN 2011
Country/Territory	United States
City	San Jose, CA
Period	7/31/11 → 8/5/11

ASJC Scopus subject areas

Software
Artificial Intelligence

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10.1109/IJCNN.2011.6033476

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Leen, TK & Friel, R 2011, Perturbation theory for stochastic learning dynamics. in 2011 International Joint Conference on Neural Networks, IJCNN 2011 - Final Program., 6033476, Proceedings of the International Joint Conference on Neural Networks, pp. 2031-2038, 2011 International Joint Conference on Neural Network, IJCNN 2011, San Jose, CA, United States, 7/31/11. https://doi.org/10.1109/IJCNN.2011.6033476

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abstract = "On-line machine learning and biological spike-timing-dependent plasticity (STDP) rules both generate Markov chains for the synaptic weights. We give a perturbation expansion (in powers of the learning rate) for the dynamics that, unlike the usual approximation by a Fokker-Planck equation (FPE), is rigorous. Our approach extends the related system size expansion by giving an expansion for the probability density as well as its moments. Applied to two observed STDP learning rules, our approach provides better agreement with Monte-Carlo simulations than either the FPE or a simple linearized theory. The approach is also applicable to stochastic neural dynamics.",

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AB - On-line machine learning and biological spike-timing-dependent plasticity (STDP) rules both generate Markov chains for the synaptic weights. We give a perturbation expansion (in powers of the learning rate) for the dynamics that, unlike the usual approximation by a Fokker-Planck equation (FPE), is rigorous. Our approach extends the related system size expansion by giving an expansion for the probability density as well as its moments. Applied to two observed STDP learning rules, our approach provides better agreement with Monte-Carlo simulations than either the FPE or a simple linearized theory. The approach is also applicable to stochastic neural dynamics.

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Perturbation theory for stochastic learning dynamics

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