Learning to Convolve: A Generalized Weight-Tying Approach
By Nichita Diaconu, Daniel E. Worrall. 2019
22 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Gabriele Cesa
- David W. Romero
- Jean-Baptiste Cordonnier
- Maurice Weiler
- Erik J. Bekkers
- Sebastian U. Stich
- Mark Hoogendoorn
- Martin Jaggi
In Computer Vision and Pattern Recognition
- David W. Romero
- Jean-Baptiste Cordonnier
- Gabriele Cesa
- Maurice Weiler
- Erik J. Bekkers
- Mark Hoogendoorn
- J. Tomczak
- Max Welling
Citations in the corpus
- Group Equivariant Stand-Alone Self-Attention For Vision (2020, background): “More recently, attention has been introduced to group equivariant architectures (Romero & Hoogendoorn, 2019; Diaconu & Worrall, 2019; Romero et al., 2020a).”
- General E(2)-Equivariant Steerable CNNs (2019, methodology): “Regular steerable CNNs were investigated for planar images in [6, 7, 8, 9, 10, 17, 18, 30], for spherical CNNs in [19, 5] and for volumetric convolutions in [31, 32].”