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 3x3 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.
Nichita Diaconu (University of Amsterdam)
Daniel E Worrall (University of Amsterdam)
Related Events (a corresponding poster, oral, or spotlight)
2019 Oral: Learning to Convolve: A Generalized Weight-Tying Approach »
Tue Jun 11th 03:05 -- 03:10 PM Room Grand Ballroom