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Main Authors: Cao, Chuxue, Yang, Jinluan, Li, Haoran, Pan, Kunhao, Zhao, Zijian, Chen, Zhengyu, Tian, Yuchen, Wu, Lijun, He, Conghui, Han, Sirui, Guo, Yike
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2601.22642
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author Cao, Chuxue
Yang, Jinluan
Li, Haoran
Pan, Kunhao
Zhao, Zijian
Chen, Zhengyu
Tian, Yuchen
Wu, Lijun
He, Conghui
Han, Sirui
Guo, Yike
author_facet Cao, Chuxue
Yang, Jinluan
Li, Haoran
Pan, Kunhao
Zhao, Zijian
Chen, Zhengyu
Tian, Yuchen
Wu, Lijun
He, Conghui
Han, Sirui
Guo, Yike
contents Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.
format Preprint
id arxiv_https___arxiv_org_abs_2601_22642
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification
Cao, Chuxue
Yang, Jinluan
Li, Haoran
Pan, Kunhao
Zhao, Zijian
Chen, Zhengyu
Tian, Yuchen
Wu, Lijun
He, Conghui
Han, Sirui
Guo, Yike
Machine Learning
Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4% and 14.2%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.
title Pushing the Boundaries of Natural Reasoning: Interleaved Bonus from Formal-Logic Verification
topic Machine Learning
url https://arxiv.org/abs/2601.22642