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Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…

Computation and Language · Computer Science 2024-03-21 Dongwei Jiang , Marcio Fonseca , Shay B. Cohen

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be…

Computation and Language · Computer Science 2023-10-20 Jinheon Baek , Soyeong Jeong , Minki Kang , Jong C. Park , Sung Ju Hwang

We introduce a new framework for Equivalence Checking (EC) of Boolean circuits based on a general technique called Logic Relaxation (LoR). The essence of LoR is to relax the formula to be solved and compute a superset S of the set of new…

Logic in Computer Science · Computer Science 2016-07-12 Eugene Goldberg

Although LLMs exhibit strong reasoning capabilities, existing training methods largely depend on outcome-based feedback, which can produce correct answers with flawed reasoning. Prior work introduces supervision on intermediate steps but…

Computation and Language · Computer Science 2026-01-30 Jundong Xu , Hao Fei , Huichi Zhou , Xin Quan , Qijun Huang , Shengqiong Wu , William Yang Wang , Mong-Li Lee , Wynne Hsu

Reinforcement learning with verifiable rewards (RLVR) improves language model reasoning by using rule-based rewards in verifiable domains such as mathematics and code. However, RLVR leads to limited generalization for open-ended tasks --…

Computation and Language · Computer Science 2025-09-25 Adithya Bhaskar , Xi Ye , Danqi Chen

Reinforcement learning (RL) has recently emerged as a compelling approach for enhancing the reasoning capabilities of large language models (LLMs), where an LLM generator serves as a policy guided by a verifier (reward model). However,…

Machine Learning · Computer Science 2025-10-24 Kaiwen Zha , Zhengqi Gao , Maohao Shen , Zhang-Wei Hong , Duane S. Boning , Dina Katabi

The most promising recent methods for AI reasoning require applying variants of reinforcement learning (RL) either on rolled out trajectories from the LLMs, even for the step-wise rewards, or large quantities of human-annotated trajectory…

Artificial Intelligence · Computer Science 2025-06-25 Sara Rajaee , Kumar Pratik , Gabriele Cesa , Arash Behboodi

Reinforcement Learning with Verifiable Rewards (RLVR) has demonstrated promising gains in enhancing the reasoning capabilities of large language models. However, its dependence on domain-specific verifiers significantly restricts its…

Computation and Language · Computer Science 2026-01-22 Chongxuan Huang , Lei Lin , Xiaodong Shi , Wenping Hu , Ruiming Tang

Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…

Logic in Computer Science · Computer Science 2025-05-30 Rolf Drechsler

LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the…

Computation and Language · Computer Science 2025-09-04 Wei Liu , Siya Qi , Xinyu Wang , Chen Qian , Yali Du , Yulan He

Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a…

Artificial Intelligence · Computer Science 2024-04-23 Lang Cao

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a promising framework for improving reasoning abilities in Large Language Models (LLMs). However, policy optimized with binary verification prone to overlook…

Machine Learning · Computer Science 2025-10-14 Jinghao Zhang , Naishan Zheng , Ruilin Li , Dongzhou Cheng , Zheming Liang , Feng Zhao , Jiaqi Wang

Verifiers--functions assigning rewards to agent behavior--have been key to AI progress in math, code, and games. However, extending gains to domains without clear-cut success criteria remains a challenge: while humans can recognize desired…

Artificial Intelligence · Computer Science 2026-03-10 Moises Andrade , Joonhyuk Cha , Brandon Ho , Vriksha Srihari , Karmesh Yadav , Zsolt Kira

Uncertainty calibration is essential for the safe deployment of large language models (LLMs), particularly when users rely on verbalized confidence estimates. While prior work has focused on classifiers or short-form generation, confidence…

Computation and Language · Computer Science 2025-06-05 Chaeyun Jang , Moonseok Choi , Yegon Kim , Hyungi Lee , Juho Lee

Answer verification is crucial not only for evaluating large language models (LLMs) by matching their unstructured outputs against standard answers, but also serves as the reward model to guide LLM optimization. Most evaluation frameworks…

Computation and Language · Computer Science 2025-08-06 Shudong Liu , Hongwei Liu , Junnan Liu , Linchen Xiao , Songyang Gao , Chengqi Lyu , Yuzhe Gu , Wenwei Zhang , Derek F. Wong , Songyang Zhang , Kai Chen

We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on…

Artificial Intelligence · Computer Science 2025-09-23 Valentin Lacombe , Valentin Quesnel , Damien Sileo

Large language models (LLMs) are increasingly used as decision-support tools in data-constrained scientific workflows, where correctness and validity are critical. However, evaluation practices often emphasize stability or reproducibility…

Machine Learning · Computer Science 2026-03-18 Nazia Riasat

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires…

Machine Learning · Computer Science 2026-04-06 Aaditya Naik , Guruprerana Shabadi , Rajeev Alur , Mayur Naik