Large language models can solve many multi-step reasoning problems, but their reasoning remains brittle: plausible intermediate steps often lead to incorrect answers. Improving reasoning at test time requires balancing two imperfect signals: the generator, which provides diversity, and the verifier, which guides correctness. Existing approaches largely favor one side of this tradeoff. Verifier-weighted voting relies on trajectories sampled from the generator and cannot steer generation toward correct ones. By contrast, beam-style verifier-guided search can steer generation, but may over-concentrate on narrow trajectory sets and amplify verifier errors. We propose Verifier-Guided Self-Consistency (VGSC), a stochastic decoding framework that combines step-level correctness and future-outcome estimates to guide reasoning during generation. VGSC repeatedly proposes candidate next steps from the base language model and uses both signals in an acceptance/resampling procedure, while maintaining multiple trajectories for final answer-level self-consistency. We provide a probabilistic interpretation of VGSC as approximate sampling from a verifier-tilted trajectory distribution. Across multiple reasoning benchmarks, generator models, and verifier families, VGSC achieves higher average accuracy than representative baselines.
Roman Vashurin, Mikhail Seleznyov, Assel Yermekova, Fedor Chernogorskii, Danila Zykov, Elena Tutubalina, Alexander Panchenko, Preslav Nakov 等 10 位作者
Classical decompositions of predictive uncertainty, such as the information-theoretic one, are defined for a fixed representation $x$ of the input object. They do not consider that $x$ may be incomplete, nor do they measure how much the missing information can affect the prediction. In Large Language Models, users can clarify an underspecified input without any retraining. The clarified input can describe the user's unobserved intent $z^*$ more accurately and change the predictive uncertainty about the outcome. In this paper, we formalize this setting probabilistically and derive a three-term decomposition of prediction risk into specification, residual aleatoric, and epistemic uncertainties. We show that at the original information level, when only $x$ is available, the aleatoric uncertainty, represented by a Bayes risk, has two components. The first, which we call specification uncertainty, is the expected reduction in this Bayes risk from revealing the intent. The second is the residual aleatoric uncertainty, i.e., the Bayes risk that remains once the intent is known, averaged over its possible values $z$ given $x$. The distinction is important, as specification uncertainty informs the decision to request clarification before making a prediction. We build approximations of these components and connect them to existing uncertainty measures. Our experiments across different domains and modalities show distinct roles for the three components. Specification uncertainty is the most informative for detecting underspecified inputs, while residual aleatoric uncertainty is the most informative for detecting in-distribution prediction errors.