We want to cover
Lie groups, lie algebras, representations
Differential Geometry (special attention to Riemannian Geometry)
Applications to Deep learning
Applications to Neuroscience
Look over each of these books (or add ones you find) and take note of which ones you prefer.
We'll compare notes and discuss next time!
Books, outlines, and papers (review this)
Original Overview Document 4154
The following are pulled directly from the original overview doc above:
Lie Theory Books
Group-Theoretical Methods in Image Understanding
Kanatani
Lie Groups, Lie Algebras, and Representations
Brian C. Hall
Diff Geom Books
Elementary Differential Geometry
Barrett O’Neill
An Introduction to Smooth Manifolds
John M. Lee
An Introduction to Manifolds
Loring W. Tu
Links Below
https://drive.google.com/drive/folders/1SC4XbT013xkSMPgin7-wh_HYef3FBWk-?usp=sharing
Also this one:
https://drive.google.com/file/d/1iGlk_jThY8VCB3QnPPgj7Us0LMaLdHCE/view?usp=sharing
[x] Pick reading material & problem assignments
[ ] List papers of interest
[ ] Organize content into weeks
[ ] Week 1 SET UP geomstats library & run an example (https://geomstats.github.io/index.html) Watch intro video (https://github.com/geomstats/geomstats) READ Lie Groups and Lie Algebras lecture notes (sections 1-3) READ Diff Geom and Lie Groups: A Computational Perspective (chapter 2)
Problems: (1),(2), and (4 or 5)
[ ] Week 2 Lie Groups and Lie Algebras lecture notes (section 4) Diff Geom and Lie Groups: A Computational Perspective (chapter 3) Problems: 1 and 2
[ ] Week 3 same pattern as above
[ ] Week 4 LieConv: https://arxiv.org/pdf/2002.12880.pdf Group Eq. CNNs https://arxiv.org/pdf/1611.08097.pdf
Sohl-Dickstein & Olshausen: https://arxiv.org/pdf/1001.1027.pdf
Sparse Manifold Transform (2018): https://arxiv.org/abs/1806.08887