Week 02 — Group Theory for Deep Learning

The minimum group theory you need to read modern equivariance papers, built from the ground up.

Lecture

Groups, subgroups, normal subgroups · group actions · representations and irreducibles · the symmetric, cyclic, dihedral, $SO(n)$, and $SE(n)$ groups · why these are the ones that matter for ML.

Read before the lecture

• Cohen and Welling, *Group Equivariant Convolutional Networks* (ICML 2016, sections 1–3)

Problem set

PS1 — Group fundamentals

1. Compute all subgroups of $D_4$ (dihedral group of the square).
2. Show that the rotation group $SO(2)$ has a single irreducible non-trivial representation in each dimension.
3. Implement the regular representation of $C_n$ as a permutation matrix.

Reference text for this week: chapter 02 of the bilingual notes — EN PDF · FR PDF.