Mechanism by which LLMs navigate P* topology (algorithmic simulation vs geometric navigation)

Determine which mechanism—active algorithmic simulation, geometric navigation over a latent kv-cache geometry, or a combination—underlies how reasoning-enhanced large language models navigate the generalized P* graph topology in planning tasks, and characterize their relative contributions.

Background

In the Discussion, the authors frame a model-agnostic inquiry into how reasoning-enhanced LLMs traverse P* structures. They present two hypotheses: (1) Active Algorithmic Simulation, where the model executes a stepwise symbolic procedure with thought tokens serving as working memory; and (2) Geometric Navigation, where the model exploits a latent spatial geometry in the kv-cache to ‘sense’ paths via topological proximity.

Although thought-trace evidence and linear scaling of reasoning tokens with plan cost support Hypothesis 1, the possibility that geometric representations contribute to efficient retrieval is not ruled out. The authors explicitly state that the overall question of mechanism remains open.