This lecture by Yann Ollivier from FAIR at Meta, Paris, explores the connections between universal optimal control, reinforcement learning, and goal-directed behavior in Large Language Models. Learn about theoretical frameworks and practical applications that bridge these fields during this 54-minute presentation hosted by the Institut des Hautes Etudes Scientifiques (IHES). Discover how mathematical principles can be applied to improve LLM performance and goal-oriented capabilities. The video is available on CARMIN.tv, a French platform specializing in mathematics and interdisciplinary scientific content with features designed specifically for researchers.