BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kathlén Kohn (KTH) DTSTART:20230215T100000Z DTEND:20230215T110000Z DTSTAMP:20260423T021048Z UID:CompAlg/6 DESCRIPTION:Title: The Geometry of Linear Convolutional Networks\nby Kathlén Kohn (KTH) as part of Machine Learning Seminar\n\n\nAbstract\nWe discuss linear convo lutional neural networks (LCNs) and their critical points. We observe that the function space (i.e.\, the set of functions represented by LCNs) can be identified with polynomials that admit certain factorizations\, and we use this perspective to describe the impact of the network’s architectur e on the geometry of the function space. For instance\, for LCNs with one- dimensional convolutions having stride one and arbitrary filter sizes\, we provide a full description of the boundary of the function space. We furt her study the optimization of an objective function over such LCNs: We cha racterize the relations between critical points in function space and in p arameter space and show that there do exist spurious critical points. We c ompute an upper bound on the number of critical points in function space u sing Euclidean distance degrees and describe dynamical invariants for grad ient descent. This talk is based on joint work with Thomas Merkh\, Guido M ontúfar\, and Matthew Trager.\n LOCATION:https://researchseminars.org/talk/CompAlg/6/ END:VEVENT END:VCALENDAR