This book is primarily based on research results that have been developed within the past eight years. Thanks to the generous startup funds from UC Berkeley (2018) and the University of Hong Kong (2023), Yi Ma was able to embark and focus on this new exciting research direction in the past eight years. Through these years, related to this research direction, Yi Ma and his research team at Berkeley have been supported by the following research grants:
The multi-university THEORINET project for the Foundations of Deep Learning, jointly funded by the Simons Foundation and the National Science Foundation (DMS grant #2031899);
The Closed-Loop Data Transcription via Minimaxing Rate Reduction project funded by the Office of Naval Research (grant N00014-22-1-2102);
The Principled Approaches to Deep Learning for Low-dimensional Structures project funded by the National Science Foundation (CISE grant #2402951).
This book would have not been possible without the financial support for these research projects. The authors have drawn tremendous inspiration from research results by colleagues and students who have been involved in these projects.