Equivariant Neural Networks Based on Moving Frames

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Equivariant Neural Networks Based on Moving Frames

Mateus SANGALLI
Postdoc, ARMINES, Paris, France
March 23rd, 2023

Abstract
Moving frames are a classical method of obtaining invariants to the action of a Lie group on a Manifold. We apply the method of moving frames to obtain equivariant or invariant neural network layers. We show two methods to obtain equivariant networks using moving frames : one uses differential invariants as their main layer and the other method uses a moving frame computed from the input image. We implement networks invariant to rotations in 2 and 3 dimensions and the methods are shown to have a better performance than a CNN on tasks where rotational invariance is important. The 3D rotation invariant networks are shown to have an increased performance than a CNN with less training data for a task of protein structure classification.

Supplementary Materials
Paper: https://proceedings.mlr.press/v197/sangalli23a.html
GitHub: https://github.com/mateussangalli/MovingFrameNetwork