equivariant

Definition

A map is equivariant when transforming the input produces the correspondingly transformed output: rotate a molecule and the predicted force vectors rotate with it. Building this into the architecture guarantees the symmetry exactly, instead of hoping augmentation teaches it approximately, and typically improves sample efficiency. Contrast invariant, where the output does not move at all — energy is invariant to rotation, forces are equivariant.

Explainers using this term

• Symmetry and Equivariance — How Group Theory Shapes Network DesignGroup Equivariant Convolutional Networks