Week 10 — Connections to TDA

Topological data analysis and geometric deep learning are coming together. What each side brings to the other.

Lecture

Persistent homology as a differentiable layer · topology-aware GNNs · sheaf neural networks (Bodnar et al. 2022) · topological message passing · open mathematical problems.

Read before the lecture

• Bodnar et al., *Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs* (NeurIPS 2022)

Recitation — paper discussion

Horn et al., *Topological Graph Neural Networks* (ICLR 2022) (paper)

Come ready to argue one side of each:

• Does the topological prior demonstrably help on benchmarks where standard GNNs fail?
• How much of the gain is the topology and how much is the auxiliary signal?

Reference text for this week: chapter 10 of the bilingual notes — EN PDF · FR PDF.