Speaker: Dr Mustafa Hajij, Santa Clara University

Title: Simplicial Tensor Networks

Abstract: Over the past decade, deep learning has been remarkably successful at solving a massive set of problems on data types including images  and sequential data. This success drove the extension of deep learning to other discrete domains such as sets, point clouds, graphs, 3D shapes, and discrete manifolds. While many of the extended schemes have successfully tackled notable challenges in each particular domain, the plethora of fragmented frameworks have created or resurfaced many long-standing problems in deep learning such as explainability, expressiveness and generalizability. Moreover, theoretical development provenover one discrete domain does not naturally apply to the other domains. Finally, the lack of a cohesive mathematical framework has created many ad hoc and inorganic implementations and ultimately limited the set of practitioners that can potentially benefit from deep learning technologies. The main objective of this talk is to introduce simplicial tensor networks, a general mathematical framework that vastly expands the domains upon which deep learning protocols can be applied, all while maintaining intuitive conceptualization, implementation and relevance to a wide range of practical applications.