Haotian Xu

Yihan Dai, Sijie Liang, Haotian Xu et al.

Large language models (LLMs) can generate executable code from natural language descriptions, but the resulting programs frequently contain bugs due to hallucinations. In the absence of formal specifications, existing approaches attempt to assess correctness using LLM-generated proxies such as tests or auto-formalized specifications. However, these proxies are produced by the same imperfect models and thus often corroborate rather than catch errors, especially when the model exhibits correlated errors. We introduce semantic triangulation, a theory-grounded framework that decorrelates model errors by transforming the original problem into a dissociative variant - one likely requiring a fundamentally different algorithm - and checks consistency between independently sampled solutions to both problems. We identify theoretical requirements for this framework, and we prove that under a formal model of LLM hallucinations, these properties confer higher confidence in program correctness. We instantiate the framework through four concrete triangulation methods based on problem inversion, decomposition, and solution enumeration. Evaluated on LiveCodeBench and CodeElo across GPT-4o, DeepSeek-V3, and Gemini 2.5 Flash, our tool increases the probability of selecting a correct program by 24% over baselines (test generation, metamorphic testing, and auto-formalized specifications) and achieves 26% higher F1 score in selection-or-abstention scenarios, while being the only method that consistently handles inexact problems admitting multiple valid solutions.

Wangtao Sun, Xiang Cheng, Xing Yu et al.

Reinforcement learning from human feedback (RLHF) is a critical technique for training large language models. However, conventional reward models based on the Bradley-Terry model (BTRM) often suffer from overconfidence when faced with inconsistent labels or out-of-distribution samples, leading to reward hacking, where the policy model blindly optimizes for proxy rewards while degrading true performance. This paper proposes the Probabilistic Uncertain Reward Model (PURM), which generalizes the Bradley-Terry model to learn the reward distributions that emerged from the preference data. We theoretically derive the loss function of PURM and introduce a novel method that uses the overlap between distributions to quantify uncertainty. Empirical results show that PURM outperforms existing methods with more accurate reward and sound uncertainty estimations, and sustains effective learning for more optimization steps and obtain higher maximum win rate in RLHF. The data and code of this paper are released at https://anonymous.4open.science/r/Probabilistic-Uncertain-Reward-Model/