用压缩方法降低数学推理标注成本，效率提升显著。
SCOPE: Compress Mathematical Reasoning Steps for Efficient Automated Process Annotation
- 将推理步骤转为代码并构建压缩前缀树，减少冗余计算
- 仅用5%资源构建19.6万样本数据集，复杂度从O(NMK)降至O(N)
- 训练的模型在多项评测中优于现有自动化方法
过程奖励模型（PRMs）在数学推理中表现优异，但现有过程标注方法（如人工标注或蒙特卡洛模拟）仍计算成本高昂。本文提出基于压缩的步骤压缩方法SCOPE，首先将自然语言推理步骤转换为代码并经抽象语法树规范化，再合并等价步骤构建前缀树。与依赖大量采样的模拟方法不同，SCOPE利用前缀树中每条根到叶路径作为训练样本，将复杂度从O(NMK)降至O(N)。我们仅用先前方法5%的计算资源构建了包含19.6万样本的大规模数据集。实验表明，基于该数据集训练的PRM在Best-of-N策略和ProcessBench评测中均持续优于现有自动化标注方法。
原文摘要 · Abstract (English)
Process Reward Models (PRMs) have demonstrated promising results in mathematical reasoning, but existing process annotation approaches, whether through human annotations or Monte Carlo simulations, remain computationally expensive. In this paper, we introduce Step COmpression for Process Estimation (SCOPE), a novel compression-based approach that significantly reduces annotation costs. We first translate natural language reasoning steps into code and normalize them through Abstract Syntax Tree, then merge equivalent steps to construct a prefix tree. Unlike simulation-based methods that waste numerous samples on estimation, SCOPE leverages a compression-based prefix tree where each root-to-leaf path serves as a training sample, reducing the complexity from $O(NMK)$ to $O(N)$. We construct a large-scale dataset containing 196K samples with only 5% of the computational resources required by previous methods. Empirical results demonstrate that PRMs trained on our dataset consistently outperform existing automated annotation approaches on both Best-of-N strategy and ProcessBench.
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