Neural Differential Equations, Control and Machine Learning

Date: Mon. April 26, 2021
Organized by: DSAD – Data Science Across Disciplines, a research group within Institute for the Future of Knowledge (IFK) at University of Johannesburg
Title: Neural Differential Equations, Control and Machine Learning

Speaker: Prof. Dr. Enrique Zuazua
Affiliation: FAU Erlangen-Nürnberg, Germany

Abstract. The seminar is focused on Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main challenges in Machine Learning and, in particular, data classification and Universal Approximation. More precisely, we adopt the perspective of the simultaneous control of systems of NODEs. We present a genuinely nonlinear and constructive method that allows an estimation of the complexity of the control strategies we develop. The very nonlinear nature of the activation functions governing the nonlinear dynamics of NODEs under consideration plays a key role. It allows deforming half of the phase space while the other half remains invariant, a property that classical models in mechanics do not fulfil. This very property allows building elementary controls inducing specific dynamics and transformations whose concatenation, along with properly chosen hyperplanes, allows achieving our goals in finitely many steps. We also present the counterparts in the control of neural transport equations, establishing a link between optimal transport and deep neural networks.

The seminar is based on work done by the speaker, Enrique Zuazua and Domènec Ruiz-Balet:
Neural ODE Control for Classification, Approximation and Transport


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