论文标题
逆问题，深度学习和对称性破坏
Inverse Problems, Deep Learning, and Symmetry Breaking
论文作者
论文摘要
在许多物理系统中，通过内在系统对称性相关的输入映射到相同的输出。当倒转此类系统时，即解决相关的逆问题时，没有唯一的解决方案。这造成了部署新兴端到端深度学习方法的根本困难。使用广义相位检索问题作为说明性示例，我们表明，仔细的对称性破坏训练数据可以帮助摆脱困难并显着提高学习绩效。我们还提取并突出提出的解决方案的基本数学原理，该原理直接适用于其他反问题。
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.
