  How can prior knowledge on the transformation invariances of a domain be
incorporated into the architecture of a neural network? We propose Equivariant
Transformers (ETs), a family of differentiable image-to-image mappings that
improve the robustness of models towards pre-defined continuous transformation
groups. Through the use of specially-derived canonical coordinate systems, ETs
incorporate functions that are equivariant by construction with respect to
these transformations. We show empirically that ETs can be flexibly composed to
improve model robustness towards more complicated transformation groups in
several parameters. On a real-world image classification task, ETs improve the
sample efficiency of ResNet classifiers, achieving relative improvements in
error rate of up to 15% in the limited data regime while increasing model
parameter count by less than 1%.
