Special Topics in AI: Geometric Deep Learning

Spring 2023

Course Description:

Exploiting geometric structure has led to the development of machine learning methods which generalize better to new situations, learn using less data, and make more physically accurate predictions. Examples of geometric techniques in deep learning include graph neural networks, convolutional neural networks, equivariant neural networks, and embeddings into Reimannian manifolds. These methods incorporate constraints to preserve geometric structure such as symmetry, curvature, or distance. This course will first provide students with the mathematical background in group theory, representation theory, and Riemannian geometry necessary to understand geometric deep learning methods. We will then study various modern techniques such as steerable convolutions, group convolutions, tensor field networks, and hyperbolic networks based on these principles. Last, we will explore the critical applications of geometric deep learning including dynamics, medical diagnosis, chemistry, and robotics.

Course Details:

Lecturer: Professor Robin Walters (r.walters@northeastern.edu)
TA: Ondrej Biza (biza.o@northeastern.edu)
Time: 11:45 AM - 1:25 PM MT
Location: Kariotis Hall 209
Piazza: https://piazza.com/northeastern/spring2023/cs7180
Office Hours:
Ondrej: ISEC room 655, Tuesday 4 to 5:30 PM, Friday 10 to 11:30 AM. Exception: Jan 17 - online on Teams.


1. CS 6140 Machine Learning
2. Familiar with linear algebra, optimization
3. Proficient with programming in Python
4. Proof writing ability

Schedule: (Graph, Grids, Groups, Gauges, Geodesics)
Date Content Reading Materials Due on Fridays
Week 1
Jan. 9 Introduction to Geometric Deep Learning DLB Chapter 6
Jan. 12 Neural Networks Review DLB Chapter 8
GNNs and CNNs
Week 2
Jan. 16 Martin Luther King Jr.'s day, no class
Jan. 19 Grids: Convolutional Networks DLB Chapter 10
Week 3
Jan. 23 Graphs: Graph Neural Networks
Jan. 26 Discussion: CNNs & GNNs HW1 due: CNN and GNN programming assignment
Equivariant NNs
Week 4
Jan. 30 Introduction to Symmetry and Deep Learning Intro to Group Theory 1
Feb. 2 Intro to Group Theory 2
Week 5
Feb. 6 Group Convolutional Networks Deep Sets and Permutation Invariance
Feb. 9 Discussion: Group-NNs HW2 due: Group problem set
Week 6
Feb. 13 Intro to Rep Theory 1
Feb. 16 Intro to Rep Theory 1 Project Proposal due
Week 7
Feb. 20 President's day, no class
Feb. 23 Steerable CNNs HW 3 due: Rep theory Problem Set
Week 8
Feb. 27 Discussion: Steerable CNNs
Mar. 2 Spherical Harmonics; Clebsh-Gordon 1 HW4 due: Steerable Programming assignment
Week 9
Mar. 6 Spring break, no class
Mar. 9 Spring break, no class
Week 10
Mar. 13 Spherical Harmonics; Clebsh-Gordon 2 Tensor Field Networks
Mar. 16 Tensor Field Networks First milestone due
Week 11
Mar. 20 Discussion: SE(3)-equivariant methods
Mar. 23 Guest Lecture Equivariance in Robotics: Ondrej, Dian
Gauge-Equivariance and Geodesics
Week 12
Mar. 27 Gauge-Equivariance
Mar. 30 Discussion: gauge-equivariance Second milestone due
Week 13
Apr. 3 Reimannian Geometry
Apr. 6 Non-Euclidean Networks and Embeddings
Week 14
Apr. 10 Discussion: non-euclidian networks
Apr. 13 Guest Lecture John Park -- Gauge Equivariant Networks
Final Evaluation
Week 15
Apr. 17 Patriot's day, no class
Apr. 20 Project presentation day final report due
Apr. 21 Project presentation day (optional makeup)

Course Assessment:

1. 50% final project.
2. 25% HW assignments.
3. 25% class paper presentation and class participation.

Final Project: (Suggested Topics)

[Latex Template]
1. Coming soon.

Geometric Deep Learning References:

1. Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges
2. Awesome Equivariant Neural Networks
3. AMMI Course of Geometric Deep Learning
4. Erik Bekkers - UvA - Geometric Deep Learning Course
5. [2010.10952] A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels

Group Theory and Representation Theory References:

1. Algebra, Second Edition, Michael Artin.pdf
2. Artin - Algebra at Northeastern
4. Hall -- Lie Groups

Deep Learning References:

1. Deep Learning Book
2. Deep Learning Course (Coursera)
3. Recurrent Neural Network
4. The Elements of Statistical Learning
5. Pattern Recognition and Machine Learning