Learning to Convolve: A Generalized Weight-Tying Approach

TL;DR

This paper introduces a learned approach to group convolutions that enables filters to be rotated and transformed efficiently, improving rotation invariance and performance on image classification tasks.

Contribution

It proposes a method to learn filter bases and their transformations, allowing flexible and accurate rotation-equivariant convolutions.

Findings

Achieves low sensitivity to input rotations in feature maps.

Maintains high classification accuracy on MNIST and CIFAR-10.

Demonstrates effective learned filter transformations for group convolutions.

Abstract

Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter on a square pixel-grid is difficult. In this paper, we learn how to transform filters for use in the group convolution, focussing on roto-translation. For this, we learn a filter basis and all rotated versions of that filter basis. Filters are then encoded by a set of rotation invariant coefficients. To rotate a filter, we switch the basis. We demonstrate we can produce feature maps with low sensitivity to input rotations, while achieving high performance on MNIST and CIFAR-10.