This $400,000 federal Project Grant award was provided by the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CISE) program (CFDA 47.070) to The Ohio State University. The grant supports collaborative research to develop a principled and unified mathematical framework for deep learning on low-dimensional data structures. The key objectives are to: 1) Design "white-box" deep neural networks optimized for information gain and representation learning, 2) Rigorously analyze the optimization objectives to guarantee correctness, and 3) Create a self-correcting, closed-loop learning system that integrates encoding and decoding. This multifaceted approach aims to bridge the gap between theory and practice in deep learning, with the goal of advancing this technology for broader applications. The project period runs from July 2024 through June 2027.