Stories in Space: In-Context Learning Trajectories in Conceptual Belief Space

TL;DR

This paper proposes that LLMs operate over a low-dimensional geometric belief space, with in-context learning as trajectories through this space, supported by behavioral and representational analyses in story understanding.

Contribution

It introduces a geometric framework for understanding belief updates in LLMs, linking internal representations to structured trajectories in conceptual space.

Findings

Belief updates follow trajectories on low-dimensional manifolds

Model behavior and internal representations reflect this structure

Interventions can causally steer belief trajectories based on geometry

Abstract

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.