BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rongjie Lai (Rensselaer Polytechnic Institute) DTSTART:20230420T160000Z DTEND:20230420T170000Z DTSTAMP:20260423T003237Z UID:MPML/101 DESCRIPTION:Title: L earning Manifold-Structured Data using Deep Neural Networks: Theory and Ap plications\nby Rongjie Lai (Rensselaer Polytechnic Institute) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\n\n\nAbstract \nDeep artificial neural networks have made great success in many problems in science and engineering. In this talk\, I will discuss our recent effo rts to develop DNNs capable of learning non-trivial geometry information h idden in data. In the first part\, I will discuss our work on advocating t he use of a multi-chart latent space for better data representation. Inspi red by differential geometry\, we propose a Chart Auto-Encoder (CAE) and p rove a universal approximation theorem on its representation capability. C AE admits desirable manifold properties that conventional auto-encoders wi th a flat latent space fail to obey. We further establish statistical guar antees on the generalization error for trained CAE models and show their r obustness to noise. Our numerical experiments also demonstrate satisfactor y performance on data with complicated geometry and topology. If time perm its\, I will discuss our work on defining convolution on manifolds via par allel transport. This geometric way of defining parallel transport convolu tion (PTC) provides a natural combination of modeling and learning on mani folds. PTC allows for the construction of compactly supported filters and is also robust to manifold deformations. I will demonstrate its applicatio ns to shape analysis and point clouds processing using PTC-nets. This talk is based on a series of joint work with my students and collaborators.\n LOCATION:https://researchseminars.org/talk/MPML/101/ END:VEVENT END:VCALENDAR