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We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the space over which a signal is defined.
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Raia Hadsell, Sumit Chopra and Yann LeCun · 2006
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“A novel set of rotationally and translationally invariant features for images based on the non-commutative bispectrum”
Risi Kondor · 2007
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“Learning the lie groups of visual invariance”
Xu Miao and Rajesh Rao · 2007
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Bernd Sturmfels · 2008
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Benjamin Culpepper and Bruno Olshausen · 2009
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“Completeness of bispectrum on compact groups”
Ramakrishna Kakarala · 2009
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“Harmonic networks: Deep translation and rotation equivariance”
Daniel Worrall, Stephan Garbin, Daniyar Turmukhambetov and Gabriel Brostow · 2017
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Chiheb Trabelsi et al · 2017
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“Cyclical learning rates for training neural networks”
Leslie Smith · 2017
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“Excessive invariance causes adversarial vulnerability”
Jörn-Henrik Jacobsen, Jens Behrmann, Richard Zemel and Matthias Bethge · 2018
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“Approximating cnns with bag-of-local-features models works surprisingly well on imagenet”
Wieland Brendel and Matthias Bethge · 2019
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Jascha Sohl-Dickstein, Ching Wang and Bruno Olshausen · 2010
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“The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach”
Ramakrishna Kakarala · 2012
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“Lie groups, Lie algebras, and representations”
Brian Hall · 2013
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“Explaining and harnessing adversarial examples”
Ian Goodfellow, Jonathon Shlens and Christian Szegedy · 2014
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“Learning the irreducible representations of commutative lie groups”
Taco Cohen and Max Welling · 2014
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Diederik Kingma and Jimmy Ba · 2014
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Adam Paszke et al · 2019
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“Disentangling images with Lie group transformations and sparse coding”
Ho Chau, Frank Qiu, Yubei Chen and Bruno Olshausen · 2020
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“Learning invariances in neural networks from training data”
Gregory Benton, Marc Finzi, Pavel Izmailov and Andrew Wilson · 2020
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“Differential Geometry and Lie Groups: A Computational Perspective”
Jean Gallier and Jocelyn Quaintance · 2020
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Kevin Musgrave, Serge Belongie and Ser-Nam Lim · 2020
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“Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges”
Michael Bronstein, Joan Bruna, Taco Cohen and Petar Veličković · 2021
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“A Group Theoretic Framework for Neural Computation”
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“CplxModule”
Ivan Nazarov and Hendrick Schroter · 2021
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