BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joan Bruna (NYU Courant) DTSTART:20210420T121500Z DTEND:20210420T134500Z DTSTAMP:20260423T022602Z UID:MathDeep/1 DESCRIPTION:Title: Mathematical aspects of neural network approximation and learning\nby Joan Bruna (NYU Courant) as part of Mathematics of Deep Learning\n\n\nAbs tract\nHigh-dimensional learning remains an outstanding phenomena where ex perimental evidence outpaces our current mathematical understanding. Neura l Networks provide a rich yet intricate class of functions with statistica l abilities to break the curse of dimensionality\, and where physical prio rs can be tightly integrated into the architecture to improve sample effic iency. Despite these advantages\, an outstanding theoretical challenge in these models is computational\, by providing an analysis that explains suc cessful optimization and generalization in the face of existing worst-case computational hardness results.\n\nIn this talk\, we will describe snippe ts of such challenge\, covering respectively optimization and approximatio n. First\, we will focus on the framework that lifts parameter optimizatio n to an appropriate measure space. We will overview existing results that guarantee global convergence of the resulting Wasserstein gradient flows\, and present our recent results that study typical fluctuations of the dyn amics around their mean field evolution\, as well as extensions of this fr amework beyond vanilla supervised learning to account for symmetries in th e function. Next\, we will discuss the role of depth in terms of approxima tion\, and present novel results establishing so-called ‘depth separatio n’ for a broad class of functions. We will conclude by discussing conseq uences in terms of optimization\, highlighting current and future mathemat ical challenges.\n\nJoint work with: Zhengdao Chen\, Grant Rotskoff\, Eric Vanden-Eijnden\, Luca Venturi\, Samy Jelassi and Aaron Zweig.\n LOCATION:https://researchseminars.org/talk/MathDeep/1/ END:VEVENT END:VCALENDAR