Check the preview of 2nd version of this platform
being developed by the open MLCommons taskforce on automation and reproducibility
as a free, open-source and technology-agnostic on-prem platform.
Deep Convolutional Neural Networks Based on Semi-Discrete Frames
lib:53e4a07a64c231c8 (v1.0.0)
Authors: Thomas Wiatowski,Helmut Bölcskei
ArXiv: 1504.05487
Document: PDF DOI
Abstract URL: http://arxiv.org/abs/1504.05487v1
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer, and proved translation-invariance as well as deformation stability of the resulting feature extractor. The purpose of this paper is to develop Mallat's theory further by allowing for different and, most importantly, general semi-discrete frames (such as, e.g., Gabor frames, wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This allows to extract wider classes of features than point singularities resolved by the wavelet transform. Our generalized feature extractor is proven to be translation-invariant, and we develop deformation stability results for a larger class of deformations than those considered by Mallat. For Mallat's wavelet-based feature extractor, we get rid of a number of technical conditions. The mathematical engine behind our results is continuous frame theory, which allows us to completely detach the invariance and deformation stability proofs from the particular algebraic structure of the underlying frames.
ArXiv: 1504.05487
Document: PDF DOI
Abstract URL: http://arxiv.org/abs/1504.05487v1
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer, and proved translation-invariance as well as deformation stability of the resulting feature extractor. The purpose of this paper is to develop Mallat's theory further by allowing for different and, most importantly, general semi-discrete frames (such as, e.g., Gabor frames, wavelets, curvelets, shearlets, ridgelets) in distinct network layers. This allows to extract wider classes of features than point singularities resolved by the wavelet transform. Our generalized feature extractor is proven to be translation-invariant, and we develop deformation stability results for a larger class of deformations than those considered by Mallat. For Mallat's wavelet-based feature extractor, we get rid of a number of technical conditions. The mathematical engine behind our results is continuous frame theory, which allows us to completely detach the invariance and deformation stability proofs from the particular algebraic structure of the underlying frames.
Relevant initiatives
Related knowledge about this paper
Reproduced results (crowd-benchmarking and competitions)
Artifact and reproducibility checklists
- ACM/cTuning artifact appendix and reproducibility checklist
- NeurIPS reproducibility checklist
- SIGPLAN's checklist for empirical evaluation
- Collective Knowledge (organizing research projects based on FAIR principles)