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.

This paper proposes to perform natural language inference with Word-Pair-Dependency-Triplets. Most previous DNN-based approaches either ignore syntactic dependency among words, or directly use tree-LSTM to generate sentence representation with irrelevant information. To overcome the problems mentioned above, we adopt Word-Pair-Dependency-Triplets to improve alignment and inference judgment. To be specific, instead of comparing each triplet from one passage with the merged information of another passage, we first propose to perform comparison directly between the triplets of the given passage-pair to make the judgement more interpretable. Experimental results show that the performance of our approach is better than most of the approaches that use tree structures, and is comparable to other state-of-the-art approaches.