Abstract
In many machine learning tasks it is desirable that a
model’s prediction transforms in an equivariant way under
transformations of its input. Convolutional neural networks
(CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint
equivariance under translations and rotations by design.
The proposed architecture employs steerable filters to ef-
ficiently compute orientation dependent responses for many
orientations without suffering interpolation artifacts from
filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize
He’s weight initialization scheme to filters which are de-
fined as a linear combination of a system of atomic filters.
Numerical experiments show a substantial enhancement of
the sample complexity with a growing number of sampled
filter orientations and confirm that the network generalizes
learned patterns over orientations. The proposed approach
achieves state-of-the-art on the rotated MNIST benchmark
and on the ISBI 2012 2D EM segmentation challenge