Week 11 — TDA and Deep Learning

Differentiable persistence, topological loss functions, and the frontier of geometric deep learning.

Lecture

Differentiable persistence (Hofer, Carrière, Royer) · topological loss functions · PersLay and TopologyLayer · open problems.

Read before the lecture

• Hofer et al., *Deep Learning with Topological Signatures* (NeurIPS 2017)
• Carrière et al., *PersLay: A Neural Network Layer for Persistence Diagrams* (AISTATS 2020)

Recitation — paper discussion

Moor, Horn, Rieck, Borgwardt, *Topological Autoencoders* (ICML 2020) (paper)

Come ready to argue one side of each:

• Does the topological regularizer materially change what an autoencoder learns?
• What's the right experimental control?

Reference text for this week: chapter 11 of the bilingual notes — EN PDF · FR PDF.