Inverse Problems, Deep Learning, and Symmetry Breaking
Inverse Problems, Deep Learning, and Symmetry Breaking
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发表时间：
2020-03
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通讯作者：
Kshitij Tayal;Chieh-Hsin Lai;Vipin Kumar;Ju Sun
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作者：
Kshitij Tayal;Chieh-Hsin Lai;Vipin Kumar;Ju Sun
在许多物理系统中，由内在系统对称性相关的输入被映射到相同的输出。当反转这样的系统时，即，解决相关的反问题，没有唯一的解决方案。这给部署新兴的端到端深度学习方法带来了根本性困难。以广义相位恢复问题为例，通过对训练数据进行对称性破缺，可以有效地克服上述困难，提高学习性能。我们还提取并突出了所提出的解决方案，这是直接适用于其他反问题的基本数学原理。
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.