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Title: Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data
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.  more » « less
Award ID(s):
1951856
NSF-PAR ID:
10174906
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
International Conference on Machine Learning
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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