Inverse Problems, Deep Learning, and Symmetry Breaking
This addresses a fundamental challenge in applying deep learning to inverse problems in physical systems, offering a generalizable solution.
The paper tackles the problem of non-unique solutions in inverse problems due to system symmetries, which hinders deep learning approaches, and demonstrates that symmetry breaking in training data significantly improves learning performance, as shown with the generalized phase retrieval example.
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.