Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space
For researchers studying in-context learning and Bayesian inference in LLMs, this work provides a geometric framework for understanding belief dynamics, though it is incremental as it builds on existing Bayesian interpretations.
The paper proposes that LLMs update beliefs over a low-dimensional geometric space during in-context learning, and shows that belief updates form structured trajectories that can be decoded from internal representations and causally steered via interventions.
Large Language Models (LLMs) update their behavior in context, which can be viewed as a form of Bayesian inference. However, the structure of the latent hypothesis space over which this inference operates remains unclear. In this work, we propose that LLMs assign beliefs over a low-dimensional geometric space - a conceptual belief space - and that in-context learning corresponds to a trajectory through this space as beliefs are updated over time. Using story understanding as a natural setting for dynamic belief updating, we combine behavioral and representational analyses to study these trajectories. We find that (1) belief updates are well-described as trajectories on low-dimensional, structured manifolds; (2) this structure is reflected consistently in both model behavior and internal representations and can be decoded with simple linear probes to predict behavior; and (3) interventions on these representations causally steer belief trajectories, with effects that can be predicted from the geometry of the conceptual space. Together, our results provide a geometric account of belief dynamics in LLMs, grounding Bayesian interpretations of in-context learning in structured conceptual representations.