Schedule
This is a tentative schedule based on the previous year and is subject to change!
Day  Title / Notes  Reading  Homework  

Tu 8/27  Introduction  
Th 8/29  Topology Basics  Riemannian Geometry Notes (Section 1)  
Tu 9/3  Topology Basics cont.  Riemannian Geometry Notes (Section 1)  HW 1, Due Tu 9/17 LaTeX source for HW 1 (for reference) 

Th 9/5  Manifold Basics  RGN (Section 2)  
Tu 9/10  Manifold Basics cont.  RGN (Section 2)  
Th 9/12  Tangent Spaces  RGN (Section 2)  
Tu 9/17  Riemannian Geometry  RGN (Section 3)  HW 1 Due  
Th 9/19  Riemannian Geometry, cont.  RGN (Section 3)  
Tu 9/24  Introduction to Shape Manifolds: Kendall’s Shape Space  Kendall, 1984  
Th 9/26  Statistics on Manifolds: Frechet Mean  Pennec, 1999  
Tu 10/1  Statistics on Manifolds: Principal Geodesic Analysis  Fletcher 2019, Section 3  
Th 10/3  Introduction to Manifold Learning: Multidimensional Scaling, Isomap 
Cayton, 2005 Tenenbaum, de Silva, Langford, 2000 

Tu 10/8  Manifold Learning: Local Linear Embedding, Laplacian Eigenmaps 
Roweis & Saul, 2000 Belkin & Niyogi, 2003 

Th 10/10  Manifold geometry of neural networks  Goodfellow et al. 2016, Chapter 14  
Tu 10/15  Reading Day – No Class  
Th 10/17  Variational Autoenconders (VAEs)  Kingma and Welling, 2014  
Tu 10/22  Lie groups  RGN (Section 4)  
Th 10/24  Lie algebras  RGN (Section 5.1) Parallel parking and Lie brackets 

Tu 10/29  Lie group actions  Applications of Lie groups: Simard, et al. 1998 Casado and Rubio, 2019 

Th 10/31  Flow based models  Glow RealNVP 

Tu 11/5  Election Day – No Class  
Th 11/7  Selfsupervised Learning  SimCLR  
Tu 11/9  ImageText Contrastive Learning  CLIP  
Th 11/14  Unsupervised Learning + Fisher information metric and Gaussians  Fisher Information Fisher Information Metric 

Tu 11/19  Natural gradients  Pascanu and Bengio, 2014 Scorebased Generative Models 

Th 11/21  Diffusion Models  Denoising Diffusion Probabilistic Models  
Tu 11/26  Graph Neural Networks  
Th 11/28  Thanksgiving – No Class  
Tu 12/3  Information theory basics, entropy  
Th 12/5  KullbackLeibler divergence 