The origin of the high performance of deep learning (generalization performance) is a big mystery. The goal of this project was to tackle it with a mathematical and applied approach. Various computer experiments related to deep learning were able to be carried out by the computer environment that was prepared by this grant project. As a result, we have accumulated practical know-how that contributes to the performance improvement of deep learning. Utilizing that know-how, we were able to conduct applied research on experimental science data, etc., while taking advantage of the strengths of machine learning. In that case, the practical side by the computer experiment was important, but the improvement and adjustment of the machine learning model by the mathematical analysis also played a big role.