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

Understand

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.