Title: Inverse Problems, Deep Learning, and Symmetry Breaking. 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 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 learning performance in real data experiments. We also extract and highlight
the underlying mathematical principle of the proposed solution, which is directly applicable to
other inverse problems. 