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In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks.
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Gtm: The generative topographic mapping
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Aapo Hyvärinen and Patrik Hoyer · 2000
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Aapo Hyvärinen and Erkki Oja · 2000
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M J Wainwright and E P Simoncelli · 2000
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Discovering multiple constraints that are frequently approximately satisfied
Geoffrey E. Hinton and Yee-Whye Teh · 2001
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Topographic independent component analysis
Aapo Hyvärinen, Patrik O Hoyer, and Mika Inki · 2001
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A two-layer sparse coding model learns simple and complex cell receptive fields and topography from natural images
Aapo Hyvärinen and Patrik O. Hoyer · 2001
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Alexei A Koulakov and Dmitri B Chklovskii · 2001
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Simple-Cell-Like Receptive Fields Maximize Temporal Coherence in Natural Video
Jarmo Hurri and Aapo Hyvärinen · 2003
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Learning sparse topographic representations with products of student-t distributions
Max Welling, Simon Osindero, and Geoffrey E Hinton · 2003
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A unifying framework for natural image statistics: spatiotemporal activity bubbles
A. Hyvärinen, J. Hurri, and Jaakko J. Väyrynen · 2004
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Contrastive Topographic Models
Simon Kayode Osindero · 2004
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Topographic Product Models Applied to Natural Scene Statistics
Simon Osindero, Max Welling, and Geoffrey E. Hinton · 2006
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Richard Turner and Maneesh Sahani · 2007
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Nonlinear image representation using divisive normalization
S Lyu and E P Simoncelli · 2008
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Overcomplete topographic independent component analysis
Libo Ma and Liqing Zhang · 2008
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Image denoising using scale mixtures of Gaussians in the wavelet domain
J Portilla, V Strela, M J Wainwright, and E P Simoncelli · 2008
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Natural image statistics: A probabilistic approach to early computational vision
Aapo Hyvärinen, Jarmo Hurri, and Patrick O Hoyer · 2009
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Harmonic networks: Deep translation and rotation equivariance
Daniel E. Worrall, Stephan J. Garbin, Daniyar Turmukhambetov, and Gabriel J. Brostow · 2017
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Towards a definition of disentangled representations
Irina Higgins, David Amos, David Pfau, Sebastien Racaniere, Loic Matthey, Danilo Rezende, and Alexander Lerchner · 2018
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Matrix capsules with EM routing
Geoffrey E Hinton, Sara Sabour, and Nicholas Frosst · 2018
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Group equivariant capsule networks
Jan Eric Lenssen, Matthias Fey, and Pascal Libuschewski · 2018
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3d steerable cnns: Learning rotationally equivariant features in volumetric data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco Cohen · 2018
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Learning to convolve: A generalized weight-tying approach
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Learning invariant features through topographic filter maps
Koray Kavukcuoglu, Marc’Aurelio Ranzato, Rob Fergus, and Yann LeCun · 2009
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Modeling multiscale subbands of photographic images with fields of Gaussian scale mixtures
S Lyu and E P Simoncelli · 2009
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Mnist handwritten digit database
Yann LeCun, Corinna Cortes, and CJ Burges · 2010
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Transforming auto-encoders
Geoffrey E. Hinton, Alex Krizhevsky, and Sida D. Wang · 2011
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Pytorch: An imperative style, high-performance deep learning library
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Deep scale-spaces: Equivariance over scale
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Learning invariances in neural networks
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Experiment tracking with weights and biases, 2020
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Variational autoencoder with embedded student- t t mixture model for authorship attribution
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Generalizing convolutional neural networks for equivariance to lie groups on arbitrary continuous data
Marc Finzi, Samuel Stanton, Pavel Izmailov, and Andrew Gordon Wilson · 2020
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Topographic deep artificial neural networks reproduce the hallmarks of the primate inferior temporal cortex face processing network
Hyodong Lee, Eshed Margalit, Kamila M. Jozwik, Michael A. Cohen, Nancy Kanwisher, Daniel L. K. Yamins, and James J. DiCarlo · 2020
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MDP homomorphic networks: Group symmetries in reinforcement learning
Elise van der Pol, Daniel E. Worrall, Herke van Hoof, Frans A. Oliehoek, and Max Welling · 2020
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Addressing the topological defects of disentanglement via distributed operators
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A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups
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Modeling category-selective cortical regions with topographic variational autoencoders
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Towards nonlinear disentanglement in natural data with temporal sparse coding
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