Schedule
Day | Title / Notes | Reading | Homework |
---|---|---|---|
Tu 8/22 | Introduction | ||
Th 8/24 | Topology Basics | Riemannian Geometry Notes (Section 1) | HW 1, Due Tu 9/12 |
Tu 8/29 | Topology Basics cont. | Riemannian Geometry Notes (Section 1) | |
Th 8/31 | Manifold Basics | RGN (Section 2) | |
Tu 9/5 | Manifold Basics cont. | RGN (Section 2) | |
Th 9/7 | Tangent Spaces | RGN (Section 2) | |
Tu 9/12 | Riemannian Geometry | RGN (Section 3) | HW 1 Due |
Th 9/14 | Riemannian Geometry, cont. | RGN (Section 3) | HW 2, Due Tu 10/10 |
Tu 9/19 | Introduction to Shape Manifolds: Kendall’s Shape Space | Kendall, 1984 | |
Th 9/21 | Statistics on Manifolds: Frechet Mean | Pennec, 1999 | |
Tu 9/26 | Statistics on Manifolds: Principal Geodesic Analysis | Fletcher 2019, Section 3 | |
Th 9/28 | Introduction to Manifold Learning: Multidimensional Scaling, Isomap |
Cayton, 2005 Tenenbaum, de Silva, Langford, 2000 |
|
Tu 10/3 | Reading Day – No Class | ||
Th 10/5 | Manifold Learning: Local Linear Embedding, Laplacian Eigenmaps |
Roweis & Saul, 2000 Belkin & Niyogi, 2003 |
Project Proposal, Due Tu 10/24 |
Tu 10/10 | Manifold geometry of neural networks Recorded Lecture (no in-person class) |
Goodfellow et al. 2016, Chapter 14 | HW 2 Due |
Th 10/12 | Variational Autoenconders (VAEs) Recorded Lecture (no in-person class) |
Kingma and Welling, 2014 | |
Tu 10/17 | Lie groups | RGN (Section 4) | |
Th 10/19 | Lie algebras | RGN (Section 5.1) Parallel parking and Lie brackets |
HW 3, Due Mon 11/6 notebook and data |
Tu 10/24 | Lie group actions | Applications of Lie groups: Simard, et al. 1998 Casado and Rubio, 2019 |
Project Proposal Due |
Th 10/26 | Flow based models | Glow RealNVP |
|
Tu 10/31 | Self-supervised Learning | SimCLR | |
Th 11/2 | Image-Text Contrastive Learning | CLIP | |
Tu 11/7 | Election Day – No Class | ||
Th 11/9 | Unsupervised Learning + Fisher information metric and Gaussians | Fisher Information Fisher Information Metric |
HW 4, Due Wed 11/22 |
Tu 11/14 | Natural gradients | Pascanu and Bengio, 2014 Score-based Generative Models |
|
Th 11/16 | Diffusion Models | Denoising Diffusion Probabilistic Models | |
Tu 11/21 | Graph Neural Networks | Final Project, Due Tu 12/5 | |
Th 11/23 | Thanksgiving – No Class | ||
Tu 11/28 | Information theory basics, entropy | ||
Th 11/30 | Kullback-Leibler divergence | ||
Tu 12/5 | Project Presentations | Final Project Reports Due |