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Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning.
Drei sätze über die n-dimensionale euklidische sphäre
Karol Borsuk · 1933
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The generalized weierstrass approximation theorem
MH Stone · 1948
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Degree Theory
N.G. Lloyd · 1978
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Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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On the approximate realization of continuous mappings by neural networks
Ken-Ichi Funahashi · 1989
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Multilayer feedforward networks are universal approximators
K. Hornik, M. Stinchcombe, and H. White · 1989
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Gaussian Processes for Machine Learning
Carl Edward Rasmussen and Christopher K. I. Williams · 2006
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Estimating or propagating gradients through stochastic neurons for conditional computation
Yoshua Bengio, Nicholas Leonard, and Aaron Courville · 2013
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Interaction Networks for Learning about Objects, Relations and Physics
Peter W. Battaglia, Razvan Pascanu, Matthew Lai, Danilo Rezende, and Koray Kavukcuoglu · 2016
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Generative adversarial nets
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2016
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A simple neural network module for relational reasoning
Adam Santoro, David Raposo, David G. T. Barrett, Mateusz Malinowski, Razvan Pascanu, Peter Battaglia, and Timothy Lillicrap · 2017
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Attention Is All You Need
Ashish Vaswani, Noam Shazeer, Niki Parmer, Jakob Uszkoreit, Lilion Jones, Aidan Gomez, Lukasz Kaiser, and Illia Polosukhin · 2017
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Deep Sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbhakhsh, Barnabás Póczos, Ruslan Salakhutdinov, and Alexander Smola · 2017
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Relational inductive biases, deep learning, and graph networks
Peter W. Battaglia, Jessica B. Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, Caglar Gulcehre, Francis Song, Andrew Ballard, Justin Gilmer, George Dahl, Ashish Vaswani, Kelsey Allen, Charles Nash, Victoria Langston, Chris Dyer, Nicolas Heess, Daan Wierstra, Pushmeet Kohli, Matt Botvinick, Oriol Vinyals, Yujia Li, and Razvan Pascanu · 2018
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Graph attention networks
Petar Veličković, Guillem Cucurull, Arantxa Casanova, Adriana Romero, Pietro Liò, and Yoshua Bengio · 2018
Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs
Ryan L Murphy, Balasubramaniam Srinivasan, Vinayak Rao, and Bruno Ribeiro · 2019
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On the Limitations of Representing Functions on Sets
Edward Wagstaff, Fabian Fuchs, Martin Engelcke, Ingmar Posner, and Michael A. Osborne · 2019
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Understanding straight-through estimator in training activation quantized neural nets
Penghang Yin, J. Lyu, S. Zhang, S. Osher, Y. Qi, and J. Xin · 2019
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Fast differentiable sorting and ranking
Mathieu Blondel, Olivier Teboul, Quentin Berthet, and Josip Djolonga · 2020
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Se(3)-transformers: 3d roto-translation equivariant attention networks
Fabian B. Fuchs, Daniel E. Worrall, Volker Fischer, and Max Welling · 2020
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Non-local graph neural networks
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Hypergcn: Hypergraph convolutional networks for semi-supervised classification
Naganand Yadati, Madhav Nimishakavi, Prateek Yadav, Anand Louis, and Partha Pratim Talukdar · 2018
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End-to-end recurrent multi-object tracking and trajectory prediction with relational reasoning
Fabian B. Fuchs, Adam R. Kosiorek, Li Sun, Oiwi Parker Jones, and Ingmar Posner · 2019
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Universal approximation of symmetric and anti-symmetric functions, 2019
Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, and Linfeng Zhang · 2019
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Set Transformer: A Framework for Attention-Based Permutation-Invariant Neural Networks
Juho Lee, Yoonho Lee, Jungtaek Kim, Adam Kosiorek, Seungjin Choi, and Yee Whye Teh · 2019
Cited alongside, same era.
Provably powerful graph networks
Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman · 2019
Cited alongside, same era.
Invariant and equivariant graph networks
Haggai Maron, Heli Ben-Hamu, Nadav Shamir, and Yaron Lipman
Cited in the paper.
PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation
Charles R Qi, Hao Su, Kaichun Mo, and Leonidas Guibas
Cited in the paper.
Meng Liu, Zhengyang Wang, and Shuiwang Ji · 2020
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Learning functions over sets via permutation adversarial networks
Chirag Pabbaraju and Prateek Jain · 2020
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On universal equivariant set networks, 2020
Nimrod Segol and Yaron Lipman · 2020
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Lambdanet: Probabilistic type inference using graph neural networks
Jiayi Wei, Maruth Goyal, Greg Durrett, and Isil Dillig · 2020
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Group equivariant stand-alone self-attention for vision
David W. Romero and Jean-Baptiste Cordonnier · 2021
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