The study of memorization in Artificial Intelligence (AI) models has become increasingly important as AI has become more widely adopted in society. This phenomenon presents significant risks, including potential privacy violations, copyright infringement, and failure to generalize beyond the limited training data. Notwithstanding its critical importance, there is a lack of understanding of the factors underlying memorization in AI, and without such understanding, the memorization problem cannot be systematically addressed, managed or mitigated. This project will develop foundational theory that will elucidate the mathematical, statistical, and contextual principles that affect memorization in AI, culminating in the development of reliable, robust, and privacy-preserving AI models. A unique aspect of the project's research framework is that it combines optimization theory, dynamical systems theory, and information theory to develop useful insights into the interplay between memorization, generalization, privacy, reproducibility, and model robustness. These insights will lead to the development of AI models that are less susceptible to privacy violations, model overfitting, and adversarial attacks, thereby enhancing the trustworthiness and applicability of AI across many domains. The investigators will integrate the research into the curriculum, engage undergraduate students in research, and hold workshops to foster collaboration and share our findings with the wider academic