%0 Generic %1 fan2018bcrnet %A Fan, Yuwei %A Bohorquez, Cindy Orozco %A Ying, Lexing %D 2018 %K audio todo:read wavelet %R 10.1016/j.jcp.2019.02.002 %T BCR-Net: a neural network based on the nonstandard wavelet form %U http://arxiv.org/abs/1810.08754 %X This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in Communications on Pure and Applied Mathematics, 44(2), 141-183. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extension, called BCR-Net, by replacing each linear sub-network with a deeper and more powerful nonlinear one. Numerical results demonstrate the efficiency of the new architecture by approximating nonlinear maps that arise in homogenization theory and stochastic computation.

@misc{fan2018bcrnet, abstract = {This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematics, 44(2), 141-183]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extension, called BCR-Net, by replacing each linear sub-network with a deeper and more powerful nonlinear one. Numerical results demonstrate the efficiency of the new architecture by approximating nonlinear maps that arise in homogenization theory and stochastic computation.}, added-at = {2022-06-20T11:10:30.000+0200}, author = {Fan, Yuwei and Bohorquez, Cindy Orozco and Ying, Lexing}, biburl = {https://www.bibsonomy.org/bibtex/2d77500f3a8204daa3ca0d8e8cb3bbae9/annakrause}, description = {1810.08754.pdf}, doi = {10.1016/j.jcp.2019.02.002}, interhash = {583a27b68f9a5cc5328223b576597928}, intrahash = {d77500f3a8204daa3ca0d8e8cb3bbae9}, keywords = {audio todo:read wavelet}, note = {cite arxiv:1810.08754Comment: 17 pages and 9 figures}, timestamp = {2022-06-20T11:12:12.000+0200}, title = {BCR-Net: a neural network based on the nonstandard wavelet form}, url = {http://arxiv.org/abs/1810.08754}, year = 2018 }