Week 07 — Equivariant and Invariant Networks

Building neural networks that commute with group actions. The cleanest case of design-by-symmetry in modern ML.

Lecture

Equivariance vs invariance · steerable kernels · $SE(3)$-transformers (Fuchs et al. 2020) · E(n)-equivariant graph neural networks (Satorras et al. 2021) · symmetry-aware molecular property prediction.

Read before the lecture

• Satorras, Hoogeboom, Welling, *E(n) Equivariant Graph Neural Networks* (ICML 2021)

Problem set

PS3 — Equivariance proofs

1. Prove that the standard CNN is equivariant to integer translations but not to general rotations.
2. Show that the E(n)-GNN of Satorras et al. is E(n)-equivariant by construction.

Reference text for this week: chapter 07 of the bilingual notes — EN PDF · FR PDF.