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Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them.
Learning lie groups for invariant visual perception
Rajesh Rao and Daniel Ruderman · 1998
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Object recognition with gradient-based learning
Yann LeCun, Patrick Haffner, Léon Bottou, and Yoshua Bengio · 1999
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Applications of Lie groups to differential equations
Peter J Olver · 2000
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An Introduction to Systems Biology: Design Principles of Biological Circuits
Uri Alon · 2006
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Greedy layer-wise training of deep networks
Y. Bengio, Pascal Lamblin, Dan Popovici, Hugo Larochelle, and U. Montreal · 2007
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An empirical evaluation of deep architectures on problems with many factors of variation
Hugo Larochelle, Dumitru Erhan, Aaron Courville, James Bergstra, and Yoshua Bengio · 2007
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Learning transport operators for image manifolds
Benjamin Culpepper and Bruno Olshausen · 2009
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Measuring invariances in deep networks
Ian Goodfellow, Honglak Lee, Quoc Le, Andrew Saxe, and Andrew Ng · 2009
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Why does unsupervised pre-training help deep learning?
Dumitru Erhan, Aaron Courville, Yoshua Bengio, and Pascal Vincent · 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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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Understanding image representations by measuring their equivariance and equivalence
Karel Lenc and Andrea Vedaldi · 2015
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Group equivariant convolutional networks
Taco Cohen and Max Welling · 2016
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Dynamic steerable blocks in deep residual networks
J-H. Jacobsen, B. de Brabandere, and A. W. M. Smeulders · 2017
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The expressive power of neural networks: A view from the width
Zhou Lu, Hongming Pu, Feicheng Wang, Zhiqiang Hu, and Liwei Wang · 2017
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On the expressive power of deep neural networks
Maithra Raghu, Ben Poole, Jon Kleinberg, Surya Ganguli, and Jascha Sohl-Dickstein · 2017
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Searching for activation functions
Prajit Ramachandran, Barret Zoph, and Quoc V. Le · 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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Error bounds for approximations with deep relu networks
Dmitry Yarotsky · 2017
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Deep sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Russ R Salakhutdinov, and Alexander J Smola · 2017
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Learning and generalization in overparameterized neural networks, going beyond two layers
Zeyuan Allen-Zhu, Yuanzhi Li, and Yingyu Liang · 2019
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Symmetry-adapted representation learning
Fabio Anselmi, Georgios Evangelopoulos, Lorenzo Rosasco, and Tomaso Poggio · 2019
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Rethinking imagenet pre-training
Kaiming He, Ross Girshick, and Piotr Dollár · 2019
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Meta-learning symmetries by reparameterization
Allan Zhou, Tom Knowles, and Chelsea Finn · 2020
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Rethinking pre-training and self-training
Barret Zoph, Golnaz Ghiasi, Tsung-Yi Lin, Yin Cui, Hanxiao Liu, Ekin Dogus Cubuk, and Quoc Le · 2020
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Automatic symmetry discovery with lie algebra convolutional network
Nima Dehmamy, Robin Walters, Yanchen Liu, Dashun Wang, and Rose Yu · 2021
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An image is worth 16x16 words: Transformers for image recognition at scale
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, and Neil Houlsby · 2021
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Residual pathway priors for soft equivariance constraints
Marc Finzi, Gregory Benton, and Andrew G Wilson · 2021
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A practical method for constructing equivariant multilayer perceptrons for arbitrary matrix groups
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Using pre-training can improve model robustness and uncertainty
Dan Hendrycks, Kimin Lee, and Mantas Mazeika · 2019
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Pytorch: An imperative style, high-performance deep learning library
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala · 2019
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General E(2)-Equivariant Steerable CNNs
Maurice Weiler and Gabriele Cesa · 2019
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Deep scale-spaces: Equivariance over scale
Daniel Worrall and Max Welling · 2019
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B-spline cnns on lie groups
Erik J Bekkers · 2020
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Representing closed transformation paths in encoded network latent space
Marissa Connor and Christopher Rozell · 2020
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Marc Finzi, Max Welling, and Andrew Gordon Wilson · 2021
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Implicit equivariance in convolutional networks
Naman Khetan, Tushar Arora, Samee Ur Rehman, and Deepak K Gupta · 2021
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Do wide and deep networks learn the same things? uncovering how neural network representations vary with width and depth
Thao Nguyen, Maithra Raghu, and Simon Kornblith · 2021
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Disco: accurate discrete scale convolutions
Ivan Sosnovik, Artem Moskalev, and Arnold Smeulders · 2021
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How to transform kernels for scale-convolutions
Ivan Sosnovik, Artem Moskalev, and Arnold Smeulders · 2021
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Scale equivariance improves siamese tracking
Ivan Sosnovik, Artem Moskalev, and Arnold W.M. Smeulders · 2021
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Mlp-mixer: An all-mlp architecture for vision
Ilya O Tolstikhin, Neil Houlsby, Alexander Kolesnikov, Lucas Beyer, Xiaohua Zhai, Thomas Unterthiner, Jessica Yung, Andreas Steiner, Daniel Keysers, Jakob Uszkoreit, et al · 2021
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Uniform generalization bounds for overparameterized neural networks
Sattar Vakili, Michael Bromberg, Jezabel Garcia, Da-shan Shiu, and Alberto Bernacchia · 2021
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Understanding deep learning (still) requires rethinking generalization
Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2021
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The lie derivative for measuring learned equivariance
Nate Gruver, Marc Finzi, Micah Goldblum, and Andrew Gordon Wilson · 2022
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Steerable partial differential operators for equivariant neural networks
Erik Jenner and Maurice Weiler · 2022
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Approximately equivariant networks for imperfectly symmetric dynamics
Rui Wang, Robin Walters, and Rose Yu · 2022
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