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In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group.
A logical calculus of the ideas immanent in nervous activity
Warren S McCulloch and Walter Pitts · 1943
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How we know universals: The perception of auditory and visual forms
Walter Pitts and Warren S McCulloch · 1947
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Receptive fields of single neurones in the cat’s striate cortex
David H Hubel and Torsten N Wiesel · 1959
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Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex
David H Hubel and Torsten N Wiesel · 1962
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Receptive fields and functional architecture of monkey striate cortex
David H Hubel and Torsten N Wiesel · 1968
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Receptive fields of single cells and topography in mouse visual cortex
Ursula C Dräger · 1975
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Spatiotemporal energy models for the perception of motion
Edward H Adelson and James R Bergen · 1985
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Roger A Horn, Roger A Horn, and Charles R Johnson · 1994
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Generalized Fourier descriptors with applications to objects recognition in SVM context
Fethi Smach, Cedric Lemaître, Jean-Paul Gauthier, Johel Miteran, and Mohamed Atri · 2008
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Bernd Sturmfels · 2008
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Completeness of bispectrum on compact groups
Ramakrishna Kakarala · 2009
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Deciphering subsampled data: adaptive compressive sampling as a principle of brain communication
Guy Isely, Christopher Hillar, and Fritz Sommer · 2010
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An unsupervised algorithm for learning Lie group transformations
Jascha Sohl-Dickstein, Ching Ming Wang, and Bruno A Olshausen · 2010
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Matrix analysis
Roger A Horn and Charles R Johnson · 2012
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The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach
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Representation theory of finite groups: an introductory approach
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A unified theory for the origin of grid cells through the lens of pattern formation
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A survey on contrastive self-supervised learning
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An overview of early vision in inceptionV1
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Actionable neural representations: Grid cells from minimal constraints
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Toroidal topology of population activity in grid cells
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Relative representations enable zero-shot latent space communication
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A toy model of universality: Reverse engineering how networks learn group operations
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