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Published online by Cambridge University Press: 29 November 2022
We give a short and concise review about the dynamical system and the control theory approach to deep learning. From the viewpoint of the dynamical systems, the back-propagation algorithm in deep learning becomes a simple consequence of the variational equations in ODEs. From the viewpoint of control theory, deep learning is a case of mean-field control in that all the agents share the same control. As an application, we discuss a new class of algorithms for deep learning based on Pontryagin’s maximum principle in control theory.
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