The Continuous Formulation of Shallow Neural Networks as Wasserstein-Type Gradient Flows

Xavier Fernández-Real () and Alessio Figalli ()
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Xavier Fernández-Real: EPFL
Alessio Figalli: ETH Zürich, Department of Mathematics

A chapter in Analysis at Large, 2022, pp 29-57 from Springer

Abstract: Abstract It has been recently observed that the training of a single hidden layer artificial neural network can be reinterpreted as a Wasserstein gradient flow for the weights for the error functional. In the limit, as the number of parameters tends to infinity, this gives rise to a family of parabolic equations. This survey aims to discuss this relation, focusing on the associated theoretical aspects appealing to the mathematical community and providing a list of interesting open problems.

Keywords: Machine learning; Continuous formulation; Gradient flow; Wasserstein distance; 35Q49; 49Q22; 68T07 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-05331-3_3

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DOI: 10.1007/978-3-031-05331-3_3

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