Week 10 — Applications

Three case studies: protein structure, neural-network loss surfaces, and gerrymandering detection.

Lecture

Protein-folding TDA features (Xia, Wei) · loss-landscape topology (Hauser et al.) · electoral-district shape via persistence · what makes an application succeed.

Read before the lecture

• Xia and Wei, *Persistent homology analysis of protein structure* (J. Chem. Phys. 2014)
• Duchin et al., *Mathematics of Districting* (preprint 2018)

Recitation — paper discussion

Hauser, Schwab et al., *On the Topology of Neural Network Loss Landscapes*

Come ready to argue one side of each:

• What does TDA see in a loss landscape that standard visualization (3-D projection) doesn't?
• Is the claim falsifiable? What would disprove it?

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