Inverse Problems, Deep Learning, and Symmetry Breaking
Machine Learning
2020-03-23 v1 Numerical Analysis
Signal Processing
Numerical Analysis
Optimization and Control
Machine Learning
Abstract
In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental difficulties for deploying the emerging end-to-end deep learning approach. Using the generalized phase retrieval problem as an illustrative example, we show that careful symmetry breaking on the training data can help get rid of the difficulties and significantly improve the learning performance. We also extract and highlight the underlying mathematical principle of the proposed solution, which is directly applicable to other inverse problems.
Cite
@article{arxiv.2003.09077,
title = {Inverse Problems, Deep Learning, and Symmetry Breaking},
author = {Kshitij Tayal and Chieh-Hsin Lai and Vipin Kumar and Ju Sun},
journal= {arXiv preprint arXiv:2003.09077},
year = {2020}
}