Schedule

Day	Title / Notes	Reading	Homework
Mo 1/12	Introduction
We 1/14	Topology Basics	Riemannian Geometry Notes (Section 1)
Mo 1/19	Happy MLK Day! – No Class
We 1/21	Topology Basics cont.	Riemannian Geometry Notes (Section 1)	HW 1, Due Wed 2/4 LaTeX source for HW 1 (for reference)
Mo 1/26	Snow Day!
We 1/28	Topology Basics cont.	RGN (Section 1)
Mo 2/2	Manifold Basics	RGN (Section 2)
We 2/4	Tangent Spaces	RGN (Section 2)	HW 1 Due
Mo 2/9	Riemannian Geometry	RGN (Section 3)
We 2/11	Riemannian Geometry cont.
Mo 2/16	Introduction to Shape Manifolds: Kendall’s Shape Space	Klingenberg, 2020
We 2/18	Statistics on Manifolds: Fréchet Mean	Pennec, 1999
Mo 2/23	Statistics on Manifolds: Principal Geodesic Analysis PCA Refresher	Fletcher 2019, Section 3
We 2/25	Introduction to Manifold Learning: Multidimensional Scaling, Isomap	Cayton, 2005 Tenenbaum, de Silva, Langford, 2000
Mo 3/2	Spring Break – No Class
We 3/4	Spring Break – No Class
Mo 3/9	Manifold Learning: Local Linear Embedding, Laplacian Eigenmaps	Roweis & Saul, 2000 Belkin & Niyogi, 2003
We 3/11	Manifold geometry of neural networks	Goodfellow et al. 2016, Chapter 14
Mo 3/16	Immersions and Submersions
We 3/18	Lie groups	RGN (Section 4)
Mo 3/23	Lie groups, cont.
We 3/25	Lie algebras	RGN (Section 5.1) Parallel parking and Lie brackets
Mo 3/30	Lie group actions	Applications of Lie groups: Simard, et al. 1998 Casado and Rubio, 2019
We 4/1	Information theory basics, entropy
Mo 4/6	Kullback-Leibler divergence
We 4/8	Fisher information metric and Gaussians	Fisher Information Fisher Information Metric
Mo 4/13	Natural gradients	Pascanu and Bengio, 2014
We 4/15	Variational Autoenconders (VAEs)	Kingma and Welling, 2014
Mo 4/20	Diffusion Models	Denoising Diffusion Probabilistic Models Score-based Generative Models
We 4/22	Sampling Methods
Mo 4/27	Langevin and Hamiltonian Monte Carlo	MALA HMC Riemannian MALA and HMC