The emerging field of geometric deep learning has put a spotlight on the role of symmetry and lowdimensional latent structures in highdimensional data analysis. In this course we start by discussing the curse of dimensionality which precludes highdimensional learning without latent structure. We then exploit symmetry: we review the basics of group representation theory and design convolutional neural networks from first principles, starting with convnets on grids and progressing over homogeneous spaces (in particular the sphere) to graphs. Finally, we connect graphs and manifolds via the Laplace–Beltrami operator and discuss the basics of spectral graph theory and graphbased clustering and manifold learning algorithms.
Timetable
Date  Topic  Resources  Assignment 

Monday 21.02.2022 
No class 


Thursday 24.02.2022  Introduction 
GGGGG Section 2.1  2.2 

Monday 28.02.2022  Basics of statistical learning  Lecture 2 of the GDL course  
Thursday 03.03.2022  Basics of statistical learning 
Lecture 2 of the GDL course; Chapter 2 of ShalevShwartz and Shai BenDavid (2014) 

Monday 07.03.2022  Fasnachtsferien  
Thursday 10.03.2022  Fasnachtsferien  
Monday 14.03.2022  ERM on finite hypothesis classes  2.3.1 of ShalevShwartz and Shai BenDavid (2014)  
Thursday 17.03.2022  ERM recap; basics of groups  The Symmetry roup of Isosceles triangle; Dihedral groups  
Monday 21.03.2022  Invariances and Equivariance on sets and graphs 
Section 4.1 of GGGGG 

Thursday 24.03.2022  Group representations; group invariance & equivariance  Section 13 of our lecture notes  
Monday 28.03.2022  Recap of group representations, invariance, and equivariance  Section 13 of our lecture notes  
Thursday 31.03.2022  Building group invariant & equivariant functions  Section 4 of our lecture notes  Problem Set 1 JupiternotebookforproblemC4 
Monday 04.04.2022  Colab and ConvNet tutorials  Colab tutorial; ConvNet tutorial  
Thursday 07.04.2022  Fourier transform and group representations  Notes by Terence Tao  
Monday 11.04.2022  Guest lecture: Truly shiftinvariant CNNs  Truly shiftinvariant CNNs  
Thursday 14.04.2022 
Ostern 

Monday 18.04.2022  Ostern  
Thursday 21.04.2022  From Fourier transform to Wavelet transform  Section 4 and 5 of our lecture notes  
Monday 25.04.2022  Section A and B of the first exercise  Solutions to problems were sent via email  
Thursday 28.04.2022  Wavelet transform; Spherical CNNs  
Monday 02.05.2022  Demo of Fourier and Wavelet transforms; Homework solutions 
Colab demo of the Fourier and Wavelet transforms Solutions to problems were sent via email. 

Thursday 05.05.2022  No class  Reading material  
Monday 09.05.2022  Spherical CNNs; exercises  
Thursday 12.05.2022  From Spherical CNN to graph neural nets  
Monday 16.05.2022  Homework exercises  
Thursday 19.05.2022  
Monday 23.05.2022  
Thursday 26.05.2022  Exercise sheet 3 (optional)  
Monday 30.05.2022  
Thursday 02.06.2022 
Resources
 Lecture notes (work in progress)
 Understanding Machine Learning: From Theory to Algorithms by Shai ShalevShwartz and Shai BenDavid
 Geometric Deep Learning Grids, Groups, Graphs, Geodesics, and Gauges by Michael M. Bronstein, Joan Bruna, Taco Cohen, Petar Veličković
 A course on Geometric Deep Learning
Contact
Lecturer
Prof. Dr. Ivan Dokmanić: ivan.dokmanic[at]unibas.ch
Teaching assistant
Tianlin Liu: t.liu[at]unibas.ch