DeepAI AI Chat
Log In Sign Up

Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data

02/25/2020
by   Marc Finzi, et al.
11

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum.

READ FULL TEXT

page 5

page 20

12/20/2020

LieTransformer: Equivariant self-attention for Lie Groups

Group equivariant neural networks are used as building blocks of group i...
02/17/2021

Group Equivariant Conditional Neural Processes

We present the group equivariant conditional neural process (EquivCNP), ...
10/07/2021

Lagrangian Neural Network with Differentiable Symmetries and Relational Inductive Bias

Realistic models of physical world rely on differentiable symmetries tha...
09/15/2021

Automatic Symmetry Discovery with Lie Algebra Convolutional Network

Existing equivariant neural networks for continuous groups require discr...
04/19/2021

A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups

Symmetries and equivariance are fundamental to the generalization of neu...
07/08/2022

Continuous Methods : Hamiltonian Domain Translation

This paper proposes a novel approach to domain translation. Leveraging e...
02/13/2023

Geometric Clifford Algebra Networks

We propose Geometric Clifford Algebra Networks (GCANs) that are based on...

Code Repositories

PointVS

SE(3)-equivariant point cloud networks for virtual screening


view repo

TepidInvariance

SE(3)-invariant neural networks for hotspot prediction


view repo

lieconv

A simple implementation of the LieConv modules in PyTorch Geometric


view repo