Understand
Using deep neural networks that are either invariant or equivariant to permutations in order to learn functions on unordered sets has become prevalent.
- The most popular, basic models are DeepSets [Zaheer et al.
- 2017] and PointNet [Qi et al.
- 2017].
Built on
Provably powerful graph networks
Haggai Maron, Heli Ben-Hamu, Hadar Serviansky, and Yaron Lipman · 1905
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Knapsack Problems: Algorithms and Computer Implementations
Silvano Martello and Paolo Toth · 1990
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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The symmetry perspective
Martin Golubitsky and Ian Stewart · 2002
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When is the algebra of multisymmetric polynomials generated by the elementary multisymmetric polynomials
Emmanuel Briand · 2004
Earlier work this paper cites.
A minimal set of generators for the ring of multisymmetric functions
David Rydh · 2007
Earlier work this paper cites.
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Charles R Qi, Hao Su, Kaichun Mo, and Leonidas J Guibas · 2017
Cited alongside, same era.
Then
Neural network with unbounded activation functions is universal approximator
Sho Sonoda and Noboru Murata · 2017
Later among the works it cites.
Deep sets
Manzil Zaheer, Satwik Kottur, Siamak Ravanbakhsh, Barnabas Poczos, Ruslan R Salakhutdinov, and Alexander J Smola · 2017
Later among the works it cites.
Universal approximations of invariant maps by neural networks
Dmitry Yarotsky · 2018
Later among the works it cites.
Universal invariant and equivariant graph neural networks
Nicolas Keriven and Gabriel Peyré · 2019
Closest in time.
Universal approximations of permutation invariant/equivariant functions by deep neural networks
Akiyoshi Sannai, Yuuki Takai, and Matthieu Cordonnier · 2019
Closest in time.
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