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Numerous invariant (or equivariant) neural networks have succeeded in handling invariant data such as point clouds and graphs.
Building symmetries into feedforward networks
John Shawe-Taylor · 1989
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Symmetries and discriminability in feedforward network architectures
John Shawe-Taylor · 1993
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Sample sizes for threshold networks with equivalences
John Shawetaylor · 1995
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Neural network learning: Theoretical foundations
Martin Anthony and Peter L Bartlett · 2009
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Spectral networks and locally connected networks on graphs
Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun · 2013
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Deep convolutional networks on graph-structured data
Mikael Henaff, Joan Bruna, and Yann LeCun · 2015
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Norm-based capacity control in neural networks
Behnam Neyshabur, Ryota Tomioka, and Nathan Srebro · 2015
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3d shapenets: A deep representation for volumetric shapes
Zhirong Wu, Shuran Song, Aditya Khosla, Fisher Yu, Linguang Zhang, Xiaoou Tang, and Jianxiong Xiao · 2015
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Group equivariant convolutional networks
Taco Cohen and Max Welling · 2016
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Machine learning energies of 2 million elpasolite (a b c 2 d 6) crystals
Felix A Faber, Alexander Lindmaa, O Anatole Von Lilienfeld, and Rickard Armiento · 2016
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Dynamical mass measurements of contaminated galaxy clusters using machine learning
Michelle Ntampaka, Hy Trac, Dougal J Sutherland, Sebastian Fromenteau, Barnabás Póczos, and Jeff Schneider · 2016
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Estimating cosmological parameters from the dark matter distribution
Siamak Ravanbakhsh, Junier B Oliva, Sebastian Fromenteau, Layne Price, Shirley Ho, Jeff G Schneider, and Barnabás Póczos · 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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Train longer, generalize better: closing the generalization gap in large batch training of neural networks
Elad Hoffer, Itay Hubara, and Daniel Soudry · 2017
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Geometric deep learning on graphs and manifolds using mixture model cnns
Federico Monti, Davide Boscaini, Jonathan Masci, Emanuele Rodola, Jan Svoboda, and Michael M Bronstein · 2017
Cited alongside, same era.
Nonparametric regression using deep neural networks with relu activation function
Johannes Schmidt-Hieber · 2017
Cited alongside, same era.
Generalization error of invariant classifiers
Jure Sokolic, Raja Giryes, Guillermo Sapiro, and Miguel Rodrigues · 2017
Cited alongside, same era.
Foldingnet: Point cloud auto-encoder via deep grid deformation
Yaoqing Yang, Chen Feng, Yiru Shen, and Dong Tian · 2018
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Universal approximations of invariant maps by neural networks
Dmitry Yarotsky · 2018
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Hierarchical graph representation learning with differentiable pooling
Zhitao Ying, Jiaxuan You, Christopher Morris, Xiang Ren, Will Hamilton, and Jure Leskovec · 2018
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Tropical geometry of deep neural networks
Liwen Zhang, Gregory Naitzat, and Lek-Heng Lim · 2018
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A general theory of equivariant cnns on homogeneous spaces
Taco S Cohen, Mario Geiger, and Maurice Weiler · 2019
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Dmitry Yarotsky · 2017
Cited alongside, same era.
Deep sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and Alexander J Smola · 2017
Cited alongside, same era.
Group equivariant capsule networks
Jan Eric Lenssen, Matthias Fey, and Pascal Libuschewski · 2018
Cited alongside, same era.
Invariant and equivariant graph networks
Haggai Maron, Heli Ben-Hamu, Nadav Shamir, and Yaron Lipman · 2018
Cited alongside, same era.
Splatnet: Sparse lattice networks for point cloud processing
Hang Su, Varun Jampani, Deqing Sun, Subhransu Maji, Evangelos Kalogerakis, Ming-Hsuan Yang, and Jan Kautz · 2018
Cited alongside, same era.
Spidercnn: Deep learning on point sets with parameterized convolutional filters
Yifan Xu, Tianqi Fan, Mingye Xu, Long Zeng, and Yu Qiao · 2018
Cited alongside, same era.
So-net: Self-organizing network for point cloud analysis
Jiaxin Li, Ben M Chen, and Gim Hee Lee
Cited in the paper.
Haggai Maron, Ethan Fetaya, Nimrod Segol, and Yaron Lipman · 2019
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Uniform convergence may be unable to explain generalization in deep learning
Vaishnavh Nagarajan and J Zico Kolter · 2019
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Universal approximations of permutation invariant/equivariant functions by deep neural networks
Akiyoshi Sannai, Yuuki Takai, and Matthieu Cordonnier · 2019
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On universal equivariant set networks
Nimrod Segol and Yaron Lipman · 2019
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On learning sets of symmetric elements
Haggai Maron, Or Litany, Gal Chechik, and Ethan Fetaya · 2020
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Universal equivariant multilayer perceptrons
Siamak Ravanbakhsh · 2020
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