Topological Deep Learning: A New Hope for AI4Science

Topological deep learning is a rapidly growing field that pertains to 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. In this talk, Tolga will present a unifying deep learning framework built upon an even richer data structure that includes widely adopted topological domains. Specifically, he will begin by introducing combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, Tolga will develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. He will additionally characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs. The performance of CCNNs on tasks related to mesh shape analysis and graph learning will be provided. The experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. These findings demonstrate the advantages of incorporating higher-order relations into deep learning models and shows great promise for AI4Science.

Online

Lifelong Learning