Group equivariant Convolutions

GroCo is a package for group equivariant convolutions. These are a special type of convolutional layers that respect a given set of symmetries.

As a simple example, consider a possible symmetry of reflections along the y-axis. A layer that is equivariant with respect to this symmetry has the property that if you feed it an image and then flip the layer’s output along the y-axis, the result is the same as flipping the input image along the y-axis and then feeding it to the layer.

Another example is the symmetry of rotations by 90 degrees. These two symmetries can be combined to produce more symmetries, forming the mathematical structure of a group. All these groups that are compatible with a regular grid are implemented in GroCo. An overview of these groups groups can be found in the Symmetries section.