Logic-Regularized Verifier Elicits Reasoning from LLMs

Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typical verifiers require resource-intensive supervised dataset construction, which is costly and faces limitations in data diversity. In this paper, we propose LOVER, an unsupervised verifier regularized by logical rules. LOVER treats the verifier as a binary latent variable, utilizing internal activations and enforcing three logical constraints on multiple reasoning paths: negation consistency, intra-group consistency, and inter-group consistency (grouped by the final answer). By incorporating logical rules as priors, LOVER can leverage unlabeled examples and is directly compatible with any offthe-shelf LLMs. Experiments on 10 datasets demonstrate that LOVER significantly outperforms unsupervised baselines, achieving performance comparable to the supervised verifier (reaching its 95% level on average). The source code is publicly available at https://github.com/ wangxinyufighting/llm-lover .