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Bruno Gavranović (May 20 2023 at 09:57):This is the topic for Tom Gebhart's guest lecture which is scheduled for May 29th:
Sheaves for AI
Abstract:
Many data-generating systems studied within machine learning derive global semantics from a collection of complex, local interactions among subsets of the system’s atomic elements. In order to properly learn representations of such systems, a machine learning algorithm must have the capacity to faithfully model these local interactions while also ensuring the resulting representations fuse properly into a consistent whole. In this talk, we will see that cellular sheaf theory offers an ideal algebro-topological framework for both 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 before turning to a discussion of sheaf (co)homology as a semi-computable tool for implementing these categorical concepts. Finally, we will observe two practical applications of these ideas in the form of sheaf neural networks, a generalization of graph neural networks for processing sheaf-valued signals; and knowledge sheaves, a sheaf-theoretic reformulation of knowledge graph embedding.
The lecture will happen at the usual time (4pm UK timezone).
See you there!
Bruno Gavranović (May 20 2023 at 09:59):Youtube link is here https://www.youtube.com/watch?v=KbTNW1L_GHE, and Zoom link is the usual one.