Predicting and Controlling Hallucination Onset in Large Language Models: A Belief-State Framework for Prospective Risk, Optimal Intervention, and Recoverability

Abstract

Hallucination mitigation in large language models (LLMs) is commonly approached through post-hoc factuality checks, uncertainty scores, token- or span-level detectors, or abstention rules. These methods are valuable but do not fully specify the sequential decision problem that arises during autoregressive generation: risk evolves over time, future observables are endogenous to the generated prefix, interventions change both the evidence process and future generation, and delayed correction may become less effective after an unsupported proposition has entered the prefix. This paper develops a decision-theoretic extension of the Latent Hallucination Hazard Model (LHHM). Hallucination onset is modeled as a partially observed semantic event with an adapted conditional hazard. We distinguish a trajectory-conditioned survival likelihood from a genuinely prospective survival forecast; the latter integrates over future observations and actions and therefore avoids treating future endogenous hazards as if they were known at the current token. A finite latent state model separates grounded, at-risk, unsupported-commitment, and repaired trajectories. Its posterior belief state supports action selection among continuation, retrieval, verification, regeneration, qualification, and abstention. We establish five limited results under explicit assumptions: a sequential survival-likelihood identity; an exact prospective survival recursion; an expected truncated time-to-onset identity; a Bayes-optimal one-step intervention condition with residual intervention risk; and the standard reduction of the partially observed process to a belief-state Markov decision process, together with contraction of the discounted Bellman operator. We do not claim a universal scalar threshold policy, a universal ``hallucination state,'' or a universal critical point. Instead, monotone action regions, pre-onset predictability, and delayed-repair degradation are posed as falsifiable hypotheses. The paper also specifies a reproducible empirical protocol using open-weight models, RAGTruth, TruthfulQA, and document-grounded generation, with temporal lead-time, calibration, recoverability, intervention efficacy, policy regret, and compute-normalized risk-coverage metrics. The framework is positioned against recent streaming and quickest-change hallucination detection: those methods ask how fast an onset can be detected, whereas the present formulation asks whether risk can be forecast before onset and which intervention minimizes expected downstream cost.