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Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning.
Invariante variationsprobleme
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Roger N. Shepard and Jacqueline Metzler · 1971
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Discovering viewpoint-invariant relationships that characterize objects
Richard Zemel and Geoffrey E Hinton · 1990
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The role of symmetry in fundamental physics
David J. Gross · 1996
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Bayesian Learning for Neural Networks
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Gradient-based learning applied to document recognition
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner · 1998
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Kenneth O. Stanley and Risto Miikkulainen · 2002
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Learning transport operators for image manifolds
Benjamin Culpepper and Bruno Olshausen · 2009
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Breaking the symmetry: Mirror discrimination for single letters but not for pictures in the visual word form area
Felipe Pegado, Kimihiro Nakamura, Laurent Cohen, and Stanislas Dehaene · 2011
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Suppression of mirror generalization for reversible letters: Evidence from masked priming
Manuel Perea, Carmen Moret-Tatay, and Victoria Panadero · 2011
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Newborn chickens generate invariant object representations at the onset of visual object experience
Justin N. Wood · 2013
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Deep symmetry networks
Robert Gens and Pedro Domingos · 2014
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Spatial transformer networks
Max Jaderberg, Karen Simonyan, Andrew Zisserman, and koray kavukcuoglu · 2015
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Group equivariant convolutional networks
Taco Cohen and Max Welling · 2016
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Breaking the curse of dimensionality with convex neural networks
Francis Bach · 2017
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Model-agnostic meta-learning for fast adaptation of deep networks
Chelsea Finn, Pieter Abbeel, and Sergey Levine · 2017
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Dynamic routing between capsules
Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton · 2017
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An unsupervised algorithm for learning Lie group transformations
Jascha Sohl-Dickstein, Ching Ming Wang, and Bruno A. Olshausen · 2017
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Revisiting unreasonable effectiveness of data in deep learning era
Chen Sun, Abhinav Shrivastava, Saurabh Singh, and Abhinav Gupta · 2017
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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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On the global convergence of gradient descent for over-parameterized models using optimal transport
Lénaïc Chizat and Francis Bach · 2018
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Classification and geometry of general perceptual manifolds
SueYeon Chung, Daniel D. Lee, and Haim Sompolinsky · 2018
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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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Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clement Hongler · 2018
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Deep neural networks as Gaussian processes
Jaehoon Lee, Jascha Sohl-dickstein, Jeffrey Pennington, Roman Novak, Sam Schoenholz, and Yasaman Bahri · 2018
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Song Mei, Andrea Montanari, and Phan-Minh Nguyen · 2018
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Learning invariances using the marginal likelihood
Mark van der Wilk, Matthias Bauer, ST John, and James Hensman · 2018
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Strike (with) a pose: Neural networks are easily fooled by strange poses of familiar objects
Michael A Alcorn, Qi Li, Zhitao Gong, Chengfei Wang, Long Mai, Wei-Shinn Ku, and Anh Nguyen · 2019
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Symmetry-adapted representation learning
Fabio Anselmi, Georgios Evangelopoulos, Lorenzo Rosasco, and Tomaso Poggio · 2019
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On exact computation with an infinitely wide neural net
Sanjeev Arora, Simon S Du, Wei Hu, Zhiyuan Li, Russ R Salakhutdinov, and Ruosong Wang · 2019
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Why do deep convolutional networks generalize so poorly to small image transformations?
Aharon Azulay and Yair Weiss · 2019
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Hamiltonian neural networks
Samuel Greydanus, Misko Dzamba, and Jason Yosinski · 2019
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A mathematical theory of semantic development in deep neural networks
Andrew M. Saxe, James L. McClelland, and Surya Ganguli · 2019
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Deep learning generalizes because the parameter-function map is biased towards simple functions
Guillermo Valle-Perez, Chico Q. Camargo, and Ard A. Louis · 2019
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Learning invariances in neural networks from training data
Gregory Benton, Marc Finzi, Pavel Izmailov, and Andrew G Wilson · 2020
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Spectrum dependent learning curves in kernel regression and wide neural networks
Blake Bordelon, Abdulkadir Canatar, and Cengiz Pehlevan · 2020
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Deep reasoning networks for unsupervised pattern de-mixing with constraint reasoning
Di Chen, Yiwei Bai, Wenting Zhao, Sebastian Ament, John Gregoire, and Carla Gomes · 2020
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Separability and geometry of object manifolds in deep neural networks
Uri Cohen, SueYeon Chung, Daniel D. Lee, and Haim Sompolinsky · 2020
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Representing closed transformation paths in encoded network latent space
Marissa Connor and Christopher Rozell · 2020
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Lagrangian neural networks
Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho · 2020
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Equivariant neural rendering
Emilien Dupont, Miguel Bautista Martin, Alex Colburn, Aditya Sankar, Josh Susskind, and Qi Shan · 2020
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Revisiting spatial invariance with low-rank local connectivity
Gamaleldin Elsayed, Prajit Ramachandran, Jonathon Shlens, and Simon Kornblith · 2020
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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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Deep learning versus kernel learning: An empirical study of loss landscape geometry and the time evolution of the neural tangent kernel
Stanislav Fort, Gintare Karolina Dziugaite, Mansheej Paul, Sepideh Kharaghani, Daniel M Roy, and Surya Ganguli · 2020
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Revisiting weakly supervised pre-training of visual perception models
Mannat Singh, Laura Gustafson, Aaron Adcock, Vinicius De Freitas Reis, Bugra Gedik, Raj Prateek Kosaraju, Dhruv Mahajan, Ross Girshick, Piotr Dollar, and Laurens Van Der Maaten · 2022
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Neural representational geometry underlies few-shot concept learning
Ben Sorscher, Surya Ganguli, and Haim Sompolinsky · 2022
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Symmetry perception by deep networks: Inadequacy of feed-forward architectures and improvements with recurrent connections
Shobhita Sundaram, Darius Sinha, Matthew Groth, Tomotake Sasaki, and Xavier Boix · 2022
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Learning invariant weights in neural networks
Tycho F.A. van der Ouderaa and Mark van der Wilk · 2022
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Approximately equivariant networks for imperfectly symmetric dynamics
Rui Wang, Robin Walters, and Rose Yu · 2022
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Sebastian Goldt, Marc Mézard, Florent Krzakala, and Lenka Zdeborová · 2020
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Progress and limitations of deep networks to recognize objects in unusual poses
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Git Re-Basin: Merging models modulo permutation symmetries
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Data symmetries and learning in fully connected neural networks
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A cookbook of self-supervised learning
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Topological obstructions and how to avoid them
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The Lie derivative for measuring learned equivariance
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Topological deep learning: Going beyond graph data
Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou, Nina Miolane, Aldo Guzmán-Sáenz, Karthikeyan Natesan Ramamurthy, Tolga Birdal, Tamal K. Dey, Soham Mukherjee, Shreyas N. Samaga, Neal Livesay, Robin Walters, Paul Rosen, and Michael T. Schaub · 2023
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On genuine invariance learning without weight-tying
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Equivariant representation learning in the presence of stabilizers
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Bispectral neural networks
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Learning layer-wise equivariances automatically using gradients
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Compositional generalization from first principles
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