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Equivariant networks capture the inductive bias about the symmetry of the learning task by building those symmetries into the model.
Size-free generalization bounds for convolutional neural networks
Philip M. Long and Hanie Sedghi · 1905
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Some limitations of norm based generalization bounds in deep neural networks
Konstantinos Pitas, Andreas Loukas, Mike Davies, and Pierre Vandergheynst · 1905
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Improved Sample Complexities for Deep Networks and Robust Classification via an All-Layer Margin
Colin Wei and Tengyu Ma · 1910
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Linear representations of finite groups
Jean-Pierre Serre · 1977
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Building symmetries into feedforward networks
J. Shawe-Taylor · 1989
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Symmetries and discriminability in feedforward network architectures
J Shawe-Taylor · 1993
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Representation theory and invariant neural networks
John Shawe-Taylor and Jeffrey Wood · 1996
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Representation theory and invariant neural networks
Jeffrey Wood and John Shawe-Taylor · 1996
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Some PAC-Bayesian Theorems
David A. McAllester · 1998
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Adaptive estimation of a quadratic functional by model selection
B. Laurent and P. Massart · 2000
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PAC-Bayes & Margins
John Langford and John Shawe-taylor · 2002
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PAC-Bayesian learning of linear classifiers
Pascal Germain, Alexandre Lacasse, François Laviolette, and Mario Marchand · 2009
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Stéphane Mallat · 2012
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User-friendly tail bounds for sums of random matrices
Joel A Tropp · 2012
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Generalization bounds for deep learning, December 2020
Guillermo Valle-Pérez and Ard A. Louis · 2012
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Group Equivariant Convolutional Networks
Taco S. Cohen and Max Welling · 2016
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Steerable CNNs
Taco S. Cohen and Max Welling · 2016
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Exploiting cyclic symmetry in convolutional neural networks
Sander Dieleman, Jeffrey De Fauw, and Koray Kavukcuoglu · 2016
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Ti-pooling: transformation-invariant pooling for feature learning in convolutional neural networks
Dmitry Laptev, Nikolay Savinov, Joachim M Buhmann, and Marc Pollefeys · 2016
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Spectrally-normalized margin bounds for neural networks
Peter L Bartlett, Dylan J Foster, and Matus J Telgarsky · 2017
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Gintare Karolina Dziugaite and Daniel M. Roy · 2017
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Generalization Error of Invariant Classifiers
Jure Sokolić, Raja Giryes, Guillermo Sapiro, and Miguel Rodrigues · 2017
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Robust Large Margin Deep Neural Networks
Jure Sokolić, Raja Giryes, Guillermo Sapiro, and Miguel Rodrigues · 2017
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Daniel E. Worrall, Stephan J. Garbin, Daniyar Turmukhambetov, and Gabriel J. Brostow · 2017
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Understanding deep learning requires rethinking generalization
Uniform convergence may be unable to explain generalization in deep learning
Vaishnavh Nagarajan and J. Zico Kolter · 2019
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General E ( 2 ) E(2) -Equivariant Steerable CNNs
Maurice Weiler and Gabriele Cesa · 2019
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B-spline CNNs on lie groups
Erik J Bekkers · 2020
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In search of robust measures of generalization
Gintare Karolina Dziugaite, Alexandre Drouin, Brady Neal, Nitarshan Rajkumar, Ethan Caballero, Linbo Wang, Ioannis Mitliagkas, and Daniel M. Roy · 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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Fantastic Generalization Measures and Where to Find Them
Yiding Jiang, Behnam Neyshabur, Dilip Krishnan, Hossein Mobahi, and Samy Bengio · 2020
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Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals · 2017
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Stronger Generalization Bounds for Deep Nets via a Compression Approach
Sanjeev Arora, Rong Ge, Behnam Neyshabur, and Yi Zhang · 2018
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Roto-translation covariant convolutional networks for medical image analysis
Erik J. Bekkers, Maxime W Lafarge, Mitko Veta, Koen A.J. Eppenhof, Josien P.W. Pluim, and Remco Duits · 2018
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A general theory of equivariant CNNs on homogeneous spaces
Taco S. Cohen, Mario Geiger, and Maurice Weiler · 2018
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Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors
Gintare Karolina Dziugaite and Daniel Roy · 2018
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Data-dependent PAC-Bayes priors via differential privacy
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Size-Independent Sample Complexity of Neural Networks
Noah Golowich, Alexander Rakhlin, and Ohad Shamir · 2018
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On the benefits of invariance in neural networks
Clare Lyle, Mark van der Wilk, Marta Kwiatkowska, Yarin Gal, and Benjamin Bloem-Reddy · 2020
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Universal equivariant multilayer perceptrons
Siamak Ravanbakhsh · 2020
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Provably strict generalisation benefit for equivariant models
Bryn Elesedy and Sheheryar Zaidi · 2021
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Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds and Benign Overfitting
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Norm-based generalisation bounds for deep multi-class convolutional neural networks
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Jeffrey Negrea, Gintare Karolina Dziugaite, and Daniel M. Roy · 2021
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Improved generalization bounds of group invariant/equivariant deep networks via quotient feature spaces
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Maurice Weiler, Patrick Forré, Erik Verlinde, and Max Welling · 2021
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Understanding the Generalization Benefit of Model Invariance from a Data Perspective
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Non-Vacuous Generalisation Bounds for Shallow Neural Networks
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A program to build e(n)-equivariant steerable CNNs
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Group symmetry in PAC learning
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