Topological Deep Learning: Going Beyond Graph Data

Mustafa Hajij, University of San Francisco, United States

Speaker	Mustafa Hajij, University of San Francisco, United States
When	Feb 11, 2025 from 11:30 AM to 12:30 PM
Where	Via zoom
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COLLOQUIUM TALK

Title: Topological Deep Learning: Going Beyond Graph Data

Abstract: Over the past decade, deep learning has been remarkably successful at solving a massive set of problems on datatypes 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 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 proven over 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. This talk introduces the foundation of topological deep learning, a rapidly growing field that is concerned with the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations including images and sequence data. It introduces the main notions while maintaining intuitive conceptualization, implementation and relevance to a wide range of practical applications. It also demonstrates the practical relevance of this framework with practical applications ranging from drug discovery to mesh and image segmentation.

Speaker Bio: Mustafa Hajij is a faculty member at the University of San Francisco, United States. Previously, he was a faculty member at Santa Clara University, United States. He has also worked at the Ohio State University, the University of South Florida, and the Louisiana State University. His research focuses on topological deep learning, topological data analysis, and geometric data processing.

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