The growing reliance on data-driven technologies across industry, science, and society demands a workforce with both strong theoretical foundations and the ability to apply rigorous statistical and mathematical reasoning to real-world problems. This Research Training Group, based in UCLA’s Department of Statistics & Data Science, will train the next generation of researchers in the mathematical and statistical foundations of data science, providing them with the tools to tackle emerging challenges in AI, biotechnology, and applied statistics. The Research Training Group will create an integrated ecosystem of research and training, engaging students at all academic levels, including high school, community college, undergraduate, graduate, and postdoctoral levels. Undergraduate students will participate in course-based research experiences and immersive summer research programs, working alongside graduate students and faculty. Graduate students and postdocs will receive comprehensive mentoring through specialized topic courses, working groups, seminars, workshops, and summer schools. A new seminar series will highlight connections between statistics, data theory, and applications across disciplines. These efforts will help build a mathematically trained workforce ready to engage with the demands of modern data science and its applications. The research project focuses on advancing the mathematical and statistical foundations of modern data science, with an emphasis on theory, methodology, and applications. In deep learning, the project will develop theory for large-scale non-convex optimization, algorithmic regularization, generalization in neural networks, and emerging phenomena such as feature learning. Foundational work on generative AI models will address scaling laws, prompt tuning, and statistical principles for in-context learning and diffusion models. The project also develops rigorous statistical methods to support trustworthy and reliable AI, as well as t