| 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. | HW 2, Due Wed 3/11 | |
| 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 | Statistics on Manifolds: PGA cont., Regression | ||
| Mo 3/2 | Spring Break -- No Class | ||
| We 3/4 | Spring Break -- No Class | ||
| Mo 3/9 | Introduction to Manifold Learning: Multidimensional Scaling |
Cayton, 2005 | |
| We 3/11 | Introduction to Manifold Learning: Isomap, Local Linear Embeddings |
Tenenbaum, de Silva, Langford, 2000 Roweis & Saul, 2000 |
HW 2 Due Fri 3/13 |
| Mo 3/16 | Manifold Learning: Laplacian Eigenmaps |
Belkin & Niyogi, 2003 | |
| We 3/18 | More Laplacian | HW 3, Due Fri 4/3 Autoencoder.ipynb teapot.pth (zipped) |
|
| Mo 3/23 | Manifold geometry of neural networks Immersions and Submersions |
Goodfellow et al. 2016, Chapter 14 | |
| We 3/25 | Lie groups | RGN (Section 4) | |
| Mo 3/30 | Lie algebras | Parallel parking and Lie brackets | |
| We 4/1 | Lie group actions | Applications of Lie groups: Simard, et al. 1998 Casado and Rubio, 2019 |
HW 3 Due Fri 4/3 |
| Mo 4/6 | Information theory basics, entropy Kullback-Leibler divergence |
HW 4, Due Mon 4/20 | |
| 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 | Sampling Methods | HW 4 Due | |
| We 4/22 | Langevin and Hamiltonian Monte Carlo | MALA HMC Riemannian MALA and HMC |
HW 5, Due Th 5/7 HW5-Starter.ipynb |
| Mo 4/27 | Diffusion Models | Denoising Diffusion Probabilistic Models Score-based Generative Models |