BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Thomas Gebhart (Minnesota) DTSTART:20230705T150000Z DTEND:20230705T160000Z DTSTAMP:20260423T021042Z UID:CompAlg/20 DESCRIPTION:Title: Specifying Local Constraints in Representation Learning with Cellular She aves\nby Thomas Gebhart (Minnesota) as part of Machine Learning Semina r\n\n\nAbstract\nMany machine learning algorithms constrain their learned representations by imparting inductive biases based on local smoothness as sumptions. While these constraints are often natural and effective\, there are situations in which their simplicity is mis-aligned with the represen tation structure required by the task\, leading to a lack of expressivity and pathological behaviors like representational oversmoothing or inconsis tency. Without a broader theoretical framework for reasoning about local r epresentational constraints\, it is difficult to conceptualize and move be yond such representational misalignments. In this talk\, we will see that cellular sheaf theory offers an ideal algebro-topological framework for bo th reasoning about and implementing machine learning models on data which are subject to such local-to-global constraints over a topological space. We will introduce cellular sheaves from a categorical perspective\, observ ing the relationship between their definition as a limit object and the co nsistency objectives underlying representation learning. We will then turn to a discussion of sheaf (co)homology as a semi-computable tool for imple menting these categorical concepts. Finally\, we will observe two practica l applications of these ideas in the form of sheaf neural networks\, a gen eralization of graph neural networks for processing sheaf-valued signals\; and knowledge sheaves\, a sheaf-theoretic reformulation of knowledge grap h embedding.\n LOCATION:https://researchseminars.org/talk/CompAlg/20/ END:VEVENT END:VCALENDAR