equivariance

A function $f(x)$ is equivariant or covariant to a transformation $t(x)$ if:

$$f(t(x))=t(f(x))$$

For example networks for per-pixel image segmentation should be equivariant to translations, rotations, flipping.

Types of equivariances:

• permutation equivariance
• translation equivariance
• rotation equivariance