无限问题生成器：通过代理工作流可验证地扩展物理推理数据
Infinite Problem Generator: Verifiably Scaling Physics Reasoning Data with Agentic Workflows
AI总结：
本文提出IPG框架，通过公式-as-代码方法生成可解物理问题，解决大语言模型训练中高质量数据稀缺的问题，发布包含1335个经典力学问题的ClassicalMechanicsV1数据集，展示高结构多样性及复杂度与代码长度的强相关性。
摘要：
训练大型语言模型进行复杂推理受限于可验证、高质量数据的稀缺性。在物理等领域，标准文本增强常引入幻觉，而静态基准缺乏用于微调所需的推理轨迹。我们引入无限问题生成器（IPG），一种代理框架，通过公式-as-代码范式生成具有保证可解性的物理问题。不同于概率文本生成，IPG将解决方案构建为可执行的Python程序，强制严格数学一致性。作为概念验证，我们发布了ClassicalMechanicsV1，一个高保真的1335个经典力学问题数据集，扩展自165个专家种子。该数据集展示了高结构多样性，涵盖102种独特的物理公式，平均每个问题包含3.05个公式。此外，我们识别出复杂度蓝图，证明公式数量与验证代码长度之间存在强线性相关性（R²≈0.95）。这种关系确立了代码复杂度作为精确、无代理的难度度量标准，使可控的课程生成成为可能。我们发布完整的IPG流程、ClassicalMechanicsV1数据集和评估报告，以支持推理密集型领域的可重复研究。
英文摘要：
Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the reasoning traces required for fine-tuning. We introduce the Infinite Problem Generator (IPG), an agentic framework that synthesizes physics problems with guaranteed solvability through a Formula-as-Code paradigm. Unlike probabilistic text generation, IPG constructs solutions as executable Python programs, enforcing strict mathematical consistency. As a proof-of-concept, we release ClassicalMechanicsV1, a high-fidelity corpus of 1,335 classical mechanics problems expanded from 165 expert seeds. The corpus demonstrates high structural diversity, spanning 102 unique physical formulas with an average complexity of 3.05 formulas per problem. Furthermore, we identify a Complexity Blueprint, demonstrating a strong linear correlation ($R^2 \approx 0.95$) between formula count and verification code length. This relationship establishes code complexity as a precise, proxy-free metric for problem difficulty, enabling controllable curriculum generation. We release the full IPG pipeline, the ClassicalMechanicsV1 dataset, and our evaluation report to support reproducible research in reasoning-intensive domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
