Title: Learning Steerable Filters for Rotation Equivariant CNNs,
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 efficiently 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 defined 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.