BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Enrique Zuazua (FAU Erlangen-Nürnberg) DTSTART:20210511T101500Z DTEND:20210511T114500Z DTSTAMP:20260423T022603Z UID:MathDeep/4 DESCRIPTION:Title: Neural Differential Equations\, Control and Machine Learning\nby Enri que Zuazua (FAU Erlangen-Nürnberg) as part of Mathematics of Deep Learnin g\n\n\nAbstract\nWe discuss Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main challe nges in Machine Learning and\, in particular\, data classification and Uni versal Approximation. More precisely\, we adopt the perspective of the sim ultaneous control of systems of NODEs. For instance\, in the context of cl assification\, each item to be classified corresponds to a different initi al datum for the Cauchy problem of the NODE. And all the solutions corresp onding the data under consideration need to be driven to the corresponding target by means of the same control. We present a genuinely nonlinear and constructive method\, allowing to estimate the complexity of the control strategies we develop. The very nonlinear nature of the activation functio ns governing the nonlinear dynamics of NODEs under consideration plays a k ey role. It allows deforming half of the phase space while the other half remains invariant\, a property that classical models in mechanics do not f ulfill. This very property allows to build elementary controls inducing sp ecific dynamics and transformations whose concatenation\, along with prope rly chosen hyperplanes\, allows achieving our goals in finitely many steps . We also present the counterparts in the context of the control of neural transport equations\, establishing a link between optimal transport and d eep neural networks.\n\nThis is a joint work Domènec Ruiz-Balet.\n LOCATION:https://researchseminars.org/talk/MathDeep/4/ END:VEVENT END:VCALENDAR