Lifted State Hypothesis in Large Language Models

Abstract

Large language models (LLMs) adapt rapidly through fine-tuning and in-context learning, yet it remains unclear which inputs they treat as the same case and why their predictions change together. We introduce the Lifted State Hypothesis. Under fixed model parameters, context scope, and target computation, samples indistinguishable in their observed computation-relevant behavior form a computation-relative type. We hypothesize that compatible episodes activate a reusable latent component---a lifted state---that supports the target computation. State reuse enables type-level generalization but creates a non-monotonic revision problem. When later evidence distinguishes a subtype, revising a state still shared with its parent may affect members whose predictions should remain unchanged. The model must separate the subtype through rerouting, a new state, or input-specific compensation. We formalize this relation between generalization and revision. We introduce the NMR-Type Dataset to evaluate LLMs. The dataset first supports a broad modulo rule. It then provides conflicting supervision for a withheld subtype while replaying earlier examples. Across full fine-tuning, LoRA, and in-context learning, models often generalize the broad rule to the subtype but fail to localize its later revision. These results provide behavioral evidence consistent with the hypothesis and motivate further study of lifted-state formation and revision.