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Mean field analysis of neural networks: a central limit theorem

Abstract:

We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural network’s fluctuations around its mean-field limit. The fluctuations have a Gaussian distribution and satisfy a stochastic partial differential equation. The proof relies upon weak...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.spa.2019.06.003

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Elsevier
Journal:
Stochastic Processes and their Applications More from this journal
Volume:
130
Issue:
3
Pages:
1820-1852
Publication date:
2019-06-12
Acceptance date:
2020-06-03
DOI:
ISSN:
0304-4149
Language:
English
Pubs id:
1124852
Local pid:
pubs:1124852
Deposit date:
2020-08-10

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