What is it about?
In machine learning for deep neural network an obvious question is: How deep need the network be? Here we give a method that helps to achieve the desired goals with a small number of layers.
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Why is it important?
A lot of expertise is available on the optimal control of systems that are governed by ordinary differential equations. This treasure of knowledge should be transported to the domain of machine learning. The vehicle to do this are neural differential equations, that are a time-coninuous version of deep neural networks.
Perspectives
While neural differential equations are studied regularly, the study of neural partial differential equations (PDEs) is less evolved. Neural PDEs allow to hava a continuous version not only of the depth of the neural network, but also of the width of the layers.
Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg
Read the Original
This page is a summary of: Optimal control of neural differential equations: The turnpike property, Systems & Control Letters, August 2026, Elsevier,
DOI: 10.1016/j.sysconle.2026.106491.
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