Georgia Institute of Technology College of Sciences

Large language models exhibit a remarkable ability to learn and adapt from context without updating their parameters. In this talk, I will present our recent work on both understanding how foundation models extract task information from context and designing contexts that enable continual improvement during inference. I will first discuss a geometric analysis on in-context learning, providing new insights into how task representations emerge and evolve across layers. I will then discuss how these insights motivate a broader paradigm of inference-time learning, in which context is actively constructed rather than passively consumed. Building on iterative refinement frameworks such as AlphaEvolve, we view context as an evolving memory that stores hypotheses, intermediate solutions, and feedback. Drawing inspiration from optimization and sequential Monte Carlo, we develop principled approaches for designing and updating context over time. Overall, understanding how models read context and how we can systematically write and evolve context may provide a foundation for the next generation of adaptive AI systems.