Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose LOVER, an unsupervised verifier regularized by logical rules. LOVER treats theverifier as a binary latent variable, utilizinginternal activations and enforcing three logical constraints on multiple reasoning paths:negation consistency, intra-group consistency,and inter-group consistency (grouped by thefinal answer). By incorporating logical rulesas priors, LOVER can leverage unlabeled examples and is directly compatible with any offthe-shelf LLMs. Experiments on 10 datasetsdemonstrate that LOVER significantly outperforms unsupervised baselines, achieving performance comparable to the supervised verifier(reaching its 95% level on average). The sourcecode is publicly available at https://github.com/wangxinyufighting/llm-lover.
@article{arxiv.2605.05893,
title = {Logic-Regularized Verifier Elicits Reasoning from LLMs},
author = {Xinyu Wang and Changzhi Sun and Lian Cheng and Yuanbin Wu and Dell Zhang and Xiaoling Wang and Xuelong Li},
journal= {arXiv preprint arXiv:2605.05893},
year = {2026}
}