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The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks.
The spectral function of an elliptic operator
Lars Hörmander · 1968
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The addition formula for the eigenfunctions of the Laplacian
Giné M. Evariste · 1975
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Wavelets and Operators , volume 1
Yves Meyer · 1993
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Embedding Riemannian manifolds by their heat kernel
Pierre Bérard, Gérard Besson, and Sylvain Gallot · 1994
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A global geometric framework for nonlinear dimensionality reduction
Joshua B. Tenenbaum, Vin de Silva, and John C. Langford · 2000
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Diffusion wavelets
Ronald R. Coifman and Mauro Maggioni · 2006
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Visualizing high-dimensional data using t-SNE
Laurens van der Maaten and Geoffrey Hinton · 2008
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Recursive interferometric representations
Stéphane Mallat · 2010
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Gradient estimate of an eigenfunction on a compact Riemannian manifold without boundary
Yiqian Shi and Bin Xu · 2010
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Unique signatures of histograms for local surface description
Federico Tombari, Samuele Salti, and Luigi Di Stefano · 2010
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Multiscale scattering for audio classification
Joakim Andén and Stéphane Mallat · 2011
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Classification with scattering operators
Joan Bruna and Stéphane Mallat · 2011
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Wavelets on graphs via spectral graph theory
David K. Hammond, Pierre Vandergheynst, and Rémi Gribonval · 2011
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Group invariant scattering
Stéphane Mallat · 2012
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Combined scattering for rotation invariant texture analysis
Laurent Sifre and Stéphane Mallat · 2012
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Invariant scattering convolution networks
Joan Bruna and Stéphane Mallat · 2013
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Rotation, scaling and deformation invariant scattering for texture discrimination
Laurent Sifre and Stéphane Mallat · 2013
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Deep scattering spectrum
Joakim Andén and Stéphane Mallat · 2014
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FAUST: Dataset and evaluation for 3D mesh registration
Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black · 2014
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Unsupervised deep Haar scattering on graphs
Xu Chen, Xiuyuan Cheng, and Stéphane Mallat · 2014
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Low dimensional manifold embedding for scattering coefficients of intrapartum fetale heart rate variability
Václav Chudácek, Ronen Talmon, Joakim Andén, Stéphane Mallat, Ronald R Coifman, Patrice Abry, and Muriel Doret · 2014
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Rigid-motion scattering for texture classification
Laurent Sifre and Stéphane Mallat · 2014
Cited alongside, same era.
Laplace-Beltrami: The Swiss army knife of geometry processing
Solid harmonic wavelet scattering: Predicting quantum molecular energy from invariant descriptors of 3D electronic densities
Michael Eickenberg, Georgios Exarchakis, Matthew Hirn, and Stéphane Mallat · 2017
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Wavelet scattering regression of quantum chemical energies
Matthew Hirn, Stéphane Mallat, and Nicolas Poilvert · 2017
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Deep functional maps: Structured prediction for dense shape correspondence
Or Litany, Tal Remez, Emanuele Rodolà, Alex Bronstein, and Michael Bronstein · 2017
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Steerable wavelet scattering for 3D atomic systems with application to Li-Si energy prediction
Xavier Brumwell, Paul Sinz, Kwang Jin Kim, Yue Qi, and Matthew Hirn · 2018
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Spherical CNNs
Taco S. Cohen, Mario Geiger, Jonas Koehler, and Max Welling · 2018
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Justin Solomon, Keenan Crane, and Etienne Vouga · 2014
Cited alongside, same era.
Audio source separation with time-frequency velocities
Guy Wolf, Stéphane Mallat, and Shihab A. Shamma · 2014
Cited alongside, same era.
Shapenet: Convolutional neural networks on non-Euclidean manifolds
Jonathan Masci, Davide Boscaini, Michael M. Bronstein, and Pierre Vandergheynst · 2015
Cited alongside, same era.
Deep roto-translation scattering for object classification
Edouard Oyallon and Stéphane Mallat · 2015
Cited alongside, same era.
B-shot: A binary feature descriptor for fast and efficient keypoint matching on 3d point clouds
Sai Manoj Prakhya, Bingbing Liu, and Weisi Lin · 2015
Cited alongside, same era.
Deep convolutional neural networks based on semi-discrete frames
Thomas Wiatowski and Helmut Bölcskei · 2015
Cited alongside, same era.
Rigid motion model for audio source separation
Guy Wolf, Stephane Mallat, and Shihab A. Shamma · 2015
Cited alongside, same era.
Solid harmonic wavelet scattering for predictions of molecule properties
Michael Eickenberg, Georgios Exarchakis, Matthew Hirn, Stéphane Mallat, and Louis Thiry · 2018
Later among the works it cites.
On the generalization of equivariance and convolution in neural networks to the action of compact groups
Risi Kondor and Shubhendu Trivedi · 2018
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Tensor field networks: Rotation- and translation-equivariant neural networks for 3d point clouds
Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley · 2018
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3D steerable cnns: Learning rotationally equivariant features in volumetric data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco Cohen · 2018
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A mathematical theory of deep convolutional neural networks for feature extraction
Thomas Wiatowski and Helmut Bölcskei · 2018
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Joint time-frequency scattering
Joakim Andén, Vincent Lostanlen, and Stéphane Mallat · 2019
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Analysis of time-frequency scattering transforms
Wojciech Czaja and Weilin Li · 2019
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Geometric scattering for graph data analysis
Feng Gao, Guy Wolf, and Matthew Hirn · 2019
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Spherical CNNs on unstructured grids
Chiyu Max Jiang, Jingwei Huang, Karthik Kashinath, Prabhat, Philip Marcus, and Matthias Niessner · 2019
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A simple approach to intrinsic correspondence learning on unstructured 3d meshes
Isaak Lim, Alexander Dielen, Marcel Campen, and Leif Kobbelt · 2019
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Understanding graph neural networks with asymmetric geometric scattering transforms
Michael Perlmutter, Feng Gao, Guy Wolf, and Matthew Hirn · 2019
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Graph convolutional neural networks via scattering
Dongmian Zou and Gilad Lerman · 2019
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