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) | HW 2, Due Th 10/10 |
| Tu 9/24 | Introduction to Shape Manifolds: Kendall’s Shape Space | Kendall, 1984 | |
| Th 9/26 | Statistics on Manifolds: Fréchet Mean | Pennec, 1999 | |
| Tu 10/1 | Statistics on Manifolds: Principal Geodesic Analysis PCA Refresher |
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 | HW 2 Due |
| Tu 10/15 | Reading Day – No Class | ||
| Th 10/17 | Immersions and Submersions | ||
| Tu 10/22 | Lie groups | RGN (Section 4) | HW 3, Due Wed 11/6 notebook and data |
| 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 | Information theory basics, entropy | ||
| Tu 11/5 | Election Day – No Class | ||
| Th 11/7 | Kullback-Leibler divergence | ||
| Tu 11/12 | Fisher information metric and Gaussians | Fisher Information Fisher Information Metric |
HW 4, Due Tu 11/26 |
| Th 11/14 | Natural gradients | Pascanu and Bengio, 2014 | |
| Tu 11/19 | |||
| Th 11/21 | Variational Autoenconders (VAEs) | Kingma and Welling, 2014 | |
| Tu 11/26 | Diffusion Models | Denoising Diffusion Probabilistic Models Score-based Generative Models |
HW 4 Due |
| Th 11/28 | Thanksgiving – No Class | ||
| Tu 12/3 | Sampling Methods | HW 5, Due Sat 12/14 at noon starter code |
|
| Th 12/5 | Langevin and Hamiltonian Monte Carlo | MALA HMC Riemannian MALA and HMC |