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Machine Learning on Geometrical Data

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27 March 2019


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Machine Learning on Geometrical Data

Schedule

Unit 1: Theories of Geometry

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

Unit 2: Applications (Student Presentations)

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

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