This $400,000 federal Project Grant award from the National Science Foundation (NSF) Computer and Information Science and Engineering (CISE) program (CFDA 47.070) supports research to develop a principled and unified mathematical framework for deep learning on low-dimensional data structures. The project aims to bridge the gap between theory and practice of deep learning by designing "white-box" deep neural networks using unrolled optimization schemes to maximize information gain in the learned representations. It will also rigorously analyze the optimization objectives and ensure consistency of the learned representations through a self-correcting closed-loop transcription framework. This work seeks to unify representation learning for discriminative, generative, and auto-encoding tasks across supervised, unsupervised, self-supervised, and continuous learning settings. The award was made to the Regents of the University of Michigan, a prominent U.S. state government-owned educational institution with extensive research capabilities, and the project will be conducted at their Ann Arbor campus over a 3-year period starting in July 2024.