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The success of convolutional networks in learning problems involving planar signals such as images is due to their ability to exploit the translation symmetry of the data distribution through weight sharing.
The Haar Integral
Nachbin, L · 1965
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Unitary Representations and Harmonic Analysis
Sugiura, Mitsuo · 1990
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Computing Fourier Transforms and Convolutions on the 2-Sphere
Driscoll, J.R. and Healy, D.M · 1994
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A Course in Abstract Harmonic Analysis
Folland, G. B · 1995
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Efficient Computation of Fourier Transforms on Compact Groups
Maslen, David K · 1998
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Fast spherical Fourier algorithms
Kunis, Stefan and Potts, Daniel · 2003
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SOFT: SO(3) Fourier Transforms
Kostelec, Peter J and Rockmore, Daniel N · 2007
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FFTs on the rotation group
Kostelec, Peter J. and Rockmore, Daniel N · 2008
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A fast algorithm for nonequispaced Fourier transforms on the rotation group
Potts, Daniel, Prestin, J, and Vollrath, A · 2009
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Magic Materials: A Theory of Deep Hierarchical Architectures for Learning Sensory Representations
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Rotation, Scaling and Deformation Invariant Scattering for Texture Discrimination
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Deep Roto-Translation Scattering for Object Classification
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Deep Learning with Sets and Point Clouds
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Harmonic Networks: Deep Translation and Rotation Equivariance
Worrall, Daniel E, Garbin, Stephan J, Turmukhambetov, Daniyar, and Brostow, Gabriel J · 2016
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Steerable CNNs
Cohen, Taco S and Welling, Max · 2017
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Solid Harmonic Wavelet Scattering for Molecular Energy Regression
Eickenberg, Michael, Exarchakis, Georgios, Hirn, Matthew, and Mallat, Stephane · 2017
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Exploiting Cyclic Symmetry in Convolutional Neural Networks
Dieleman, S., De Fauw, J., and Kavukcuoglu, K · 2016
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Zhou, Yanzhao, Ye, Qixiang, Qiu, Qiang, and Jiao, Jianbin · 2017
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