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	Self-supervised Learning	SimCLR
Tu 11/9	Image-Text 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 Score-based 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	Kullback-Leibler divergence