Topological Deep Learning: Going Beyond Graph Data

Explore topological deep learning in this comprehensive lecture on developing deep learning models for data supported on topological domains. Dive into efficient message passing over long ranges, neighborhood functions, and bridging gaps between higher-order domains. Learn about CC-Embeddings for enriching domains and the differences between continuous and discrete neighborhoods. Gain insights into Combinatorial Complex Neural Networks, including CC-Pooling and CC-Unpooling techniques. Examine practical applications through mesh segmentation results before participating in a Q&A session. Discover how this unifying deep learning framework built on rich data structures can be applied to simplicial complexes, cell complexes, and hypergraphs, generalizing many domains encountered in scientific computations.

- Intro
- Efficient Message Passing Over Long Range
- Neighborhood Functions
- Bridging the Gap Between Higher-Order Domains
- CC-Embeddings: Enriching Domains
- Continous vs. Discrete Neighborhoods
- Intro to Combinatorial Complex Neural Networks
- CC-Pooling and CC-Unpooling
- Mesh Segmentation: Results
- Q+A