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Machine Learning on Geometrical Data

1/8	Introduction	overview of the course, logistics, introduction to deep learning
1/10	Numerical Methods	linear system, optimization. slides credit: Prof. Justin Solomon from MIT
1/15	Curves	curve theory, Frenet frame. slides credit: Prof. Justin Solomon from MIT. Reference: Intro to DG, Ch2
1/17	Surfaces, First Fundamental Form	surface theory, first fundamental form. slides credit: Prof. Keenan Crane from CMU. References: Intro to DG, Ch3, 4, 5
1/22	Second Fundamental Form	second fundamental form, gaussian curvature. slides credit: Prof. Keenan Crane from CMU. References: Intro to DG, Ch3, 4, 5
1/24	Theorema Egregium and Gauss-Bonnet	intrinsic geometry, theorema egregium, euler characteristic, angle excess theorem, gauss-bonnet theorem. References: Intro to DG, Ch6
1/29	Geodesics	theories of geodesic, fast marching algorithm
1/31	Laplacian Operator	divergence on manifolds, heat equation, laplacian-bertrami operator, harmonic functions. reference: Analysis on Manifolds via the Laplacian
2/5	Laplacian and Applications	laplacian graph theory and practice
2/7	Data Embedding	classical embedding theorems and typical algorithms. reference: Note
2/12	High-dimensional Geometry	some odd behaviors in high-dimensional geometry. reference: Ch 2

2/14	Laplacian for Graph Embedding	Laplacian Surface Editing; The Laplacian in RL: Learning Representations with Efficient Approximations
2/19	Graph Convolutional Neural Networks	Diffusion-Convolutional Neural Networks; Graph attention networks; Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks
2/21	Convolution on meshes	Orbifold Tutte Embeddings; Spherical Orbifold Tutte Embeddings; Convolutional Neural Networks on Surfaces via Seamless Toric Covers
2/26	Deep learning on Point Cloud	PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation; A Point Set Generation Network for 3D Object Reconstruction from a Single Image; Learning Free-Form Deformations for 3D Object Reconstruction
2/28	Optimal Transport	Optimal Transport: A Crash Course (up to P42); reference: Computational Optimal Transport
3/5	Embedding Learning by Optimal Transport	Learning Wasserstein Embeddings; Learning Entropic Wasserstein Embeddings
3/7	Geometry of GAN	A Geometric View of Optimal Transportation and Generative Model
3/12	Geometry and Topology Analysis of Neural Networks	Empirical study of the topology and geometry of deep networks; Exponential expressivity in deep neural networks through transient chaos
3/14	Relating Geometries by Functional maps	Functional Maps: A Flexible Representation of Maps Between Shapes; Improved functional mappings via product preservation