Unsupervised reinforcement learning (RL) has emerged as a promising paradigm for enabling self-improvement in large language models (LLMs). However, existing unsupervised RL-based methods often lack the capacity to adapt to the model’s evolving reasoning capabilities during training. Therefore, these methods can misdirect policy optimization in the absence of ground-truth supervision. To address this issue, we introduce FREIA, a novel RL-based algorithm built on two key innovations: (1) Free Energy-Driven Reward (FER) adapts rewards to balance consensus and exploration based on the Free Energy Principle. (2) Adaptive Advantage Shaping (AAS) adaptively adjusts learning signals based on the statistical characteristics of sampled rewards. Empirical evaluations on nine datasets across three reasoning tasks showcase that FREIA outperforms other unsupervised RL-based baselines. Notably, in mathematical reasoning tasks, FREIA surpasses other methods by an average of 0.5 to 3.5 points in Pass@1 using the DeepSeek-R1-Distill-Qwen-1.5B model.

Large language models (LLMs) demonstrate considerable proficiency in numerous coding-related tasks; however, their capabilities in detecting software vulnerabilities remain limited. This limitation primarily stems from two factors: (1) the absence of reasoning data related to vulnerabilities, which hinders the models’ ability to capture underlying vulnerability patterns; and (2) their focus on learning semantic representations rather than the reason behind them, thus failing to recognize semantically similar vulnerability samples. Furthermore, the development of LLMs specialized in vulnerability detection is challenging, particularly in environments characterized by the scarcity of high-quality datasets. In this paper, we propose a novel framework ReVD that excels at mining vulnerability patterns through reasoning data synthesizing and vulnerability-specific preference optimization. Specifically, we construct forward and backward reasoning processes for vulnerability and corresponding fixed code, ensuring the synthesis of high-quality reasoning data. Moreover, we design the triplet supervised fine-tuning followed by curriculum online preference optimization for enabling ReVD to better understand vulnerability patterns. The extensive experiments conducted on PrimeVul and SVEN datasets demonstrate that ReVD sets new state-of-the-art for LLM-based software vulnerability detection, e.g., 12.24%-22.77% improvement in the accuracy. The source code and data are available at https://github.com/Xin-Cheng-Wen/PO4Vul.