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Permutation-invariant, -equivariant, and -covariant functions and anti-symmetric functions are important in quantum physics, computer vision, and other disciplines.
The Classical Groups: Their Invariants and Representations
Hermann Weyl · 1946
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On the Reprepsentation of Continuous Functions of Several Variables as Superpositions of Continuous Functions of One Variable and Addition
Andrej Kolmogorov · 1957
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Universal approximation bounds for superpositions of a sigmoidal function
A.R. Barron · 1993
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Analysis and design of an analog sorting network
Jun Wang · 1995
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Random Approximants and Neural Networks
Y. Makovoz · 1996
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Approximation theory of the MLP model in neural networks
Allan Pinkus · 1999
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Kolmogorov superposition theorem and its applications
Xing Liu · 2016
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Error bounds for approximations with deep ReLU networks
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Computation for the Kolmogorov Superposition Theorem
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Deep Neural Network Approximation Theory
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Universal approximation of symmetric and anti-symmetric functions
Jiequn Han, Yingzhou Li, Lin Lin, Jianfeng Lu, Jiefu Zhang, and Linfeng Zhang · 2019
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Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
David Pfau, James S. Spencer, Alexander G. de G. Matthews, and W. M. C. Foulkes · 2019
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Akiyoshi Sannai and Masaaki Imaizumi · 2019
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On the Limitations of Representing Functions on Sets
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Edward Wagstaff, Fabian B. Fuchs, Martin Engelcke, Ingmar Posner, and Michael Osborne · 2019
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Deep Network Approximation for Smooth Functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
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