Скачать или смотреть Equivariant Convolutions and Tensor Fields — Episode 3: Rotational Equivariance

0:00 Standard convolutions are not rotationally equivariant
0:22 Rotational equivariance condition
0:50 The general setting and the coordinates
1:47 Pullback
2:46 Geometric derivation of the rotational equivariance condition
9:04 Visual example of a rotationally equivariant kernel

This video series introduces the mathematical and conceptual foundations of equivariant convolutions, with a focus on rotational and translational equivariance as used in model architectures built for applications in physics, chemistry, and materials science.

The goal of the series is to build a clear, first-principles understanding of how symmetry constraints are encoded in modern neural network architectures, progressing from familiar CNNs and discrete convolutions to 2D harmonic convolutions to tensor field networks and providing a foundation for understanding state-of-the-art equivariant interatomic potentials.

Watch the full video series here:
   • Equivariant Convolutions and Tensor Fields  

Code for the animations in this series:
https://github.com/teerev/equivariant...

Presenter: Trevor Hardcastle
LinkedIn:   / trevor-hardcastle  
GitHub: https://github.com/teerev/
Google Scholar: https://scholar.google.com/citations?...

References and related work:

Harmonic Networks
D. E. Worrall et al., Harmonic Networks: Deep Translation and Rotation Equivariance (2017).
https://arxiv.org/abs/1612.04642

Tensor Field Networks
N. Thomas et al., Tensor Field Networks: Rotation- and Translation-Equivariant Neural Networks for 3D Point Clouds (2018).
https://arxiv.org/abs/1802.08219

NequIP
S. Batzner et al., E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials, Nature Communications 13, 2453 (2022).
https://www.nature.com/articles/s4146...

MACE
I. Batatia et al., MACE: Higher-Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields (NeurIPS 2022).
https://arxiv.org/abs/2206.07697

Allegro
A. Musaelian et al., Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics, Nature Communications 14, 579 (2023).
https://www.nature.com/articles/s4146...

Equivariant Deep Learning Made Easy
O. T. Unke and H. Maennel, E(3)-Equivariant Deep Learning Made Easy (2024).
https://arxiv.org/abs/2401.07595