Enhancing the mathematical reasoning capabilities of Large Language Models (LLMs) is of great scientific and practical significance. Researchers typically employ process-supervised reward models (PRMs) to guide the reasoning process, effectively improving the models’ reasoning abilities. However, existing methods for constructing process supervision training data, such as manual annotation and per-step Monte Carlo estimation, are often costly or suffer from poor quality. To address these challenges, this paper introduces a framework called EpicPRM (Efficient, Precise, Cheap), which annotates each intermediate reasoning step based on its quantified contribution and uses an adaptive binary search algorithm to enhance both annotation precision and efficiency. Using this approach, we efficiently construct a high-quality process supervision training dataset named Epic50k, consisting of 50k annotated intermediate steps. Compared to other publicly available datasets, the PRM trained on Epic50k demonstrates significantly superior performance.

Generative conversation systems tend to produce meaningless and generic responses, which significantly reduce the user experience. In order to generate informative and diverse responses, recent studies proposed to fuse knowledge to improve informativeness and adopt latent variables to enhance the diversity. However, utilizing latent variables will lead to the inaccuracy of knowledge in the responses, and the dissemination of wrong knowledge will mislead the communicators. To address this problem, we propose a Syntactically Diverse Adversarial Network (SDAN) for knowledge-grounded conversation model. SDAN contains an adversarial hierarchical semantic network to keep the semantic coherence, a knowledge-aware network to attend more related knowledge for improving the informativeness and a syntactic latent variable network to generate syntactically diverse responses. Additionally, in order to increase the controllability of syntax, we adopt adversarial learning to decouple semantic and syntactic representations. Experimental results show that our model can not only generate syntactically diverse and knowledge-accurate responses but also significantly achieve the balance between improving the syntactic diversity and maintaining the knowledge accuracy.