逻辑结构作为知识：通过结构化逻辑知识密度估计增强LLM推理
Logical Structure as Knowledge: Enhancing LLM Reasoning via Structured Logical Knowledge Density Estimation
AI总结：
本文提出通过结构化逻辑知识密度估计提升LLM推理能力，通过增强逻辑密度而非扩大数据量来提高模型认知潜力。
摘要：
大型语言模型（LLMs）的推理能力日益归因于训练数据质量而非单纯的参数扩展。然而，现有的数据导向范式往往将质量等同于事实性或多样性，并忽视了训练样本的内部逻辑复杂性。在本工作中，我们提出自然语言通过蕴含关系和逻辑拓扑表现出结构化逻辑知识。为了量化这一点，我们引入了结构化逻辑知识密度（SLKD），一种新的度量标准，通过将自然语言分解为可执行谓词和逻辑原语来衡量逻辑信息内容。我们的分析揭示了当前数据集中存在显著的逻辑差异，其中稀疏的逻辑信号占主导地位。因此，我们提出了一种密度感知的重新识别优化策略，优先选择高密度逻辑样本以增强LLM的推理能力。广泛的实验表明，我们的方法在不增加总数据量的情况下提升了推理性能和泛化能力。这些结果进一步在强化学习框架中得到验证，表明提高逻辑密度比扩大数据规模对实现LLM的全部认知潜力更为关键。发布的代码可在附录C中找到。
英文摘要：
The reasoning capabilities of Large Language Models (LLMs) are increasingly attributed to training data quality rather than mere parameter scaling. However, existing data-centric paradigms often equate quality with factuality or diversity and ignore the internal logical complexity of training samples. In this work, we propose that natural language harbors Structured Logical Knowledge manifested through entailment relationships and logical topologies. To quantify this, we introduce Structured Logical Knowledge Density (SLKD), a novel metric that measures logical information content by decomposing natural language into executable predicates and logical primitives. Our analysis reveals a significant logical disparity in current datasets where sparse logical signals predominate. Consequently, we propose a density aware re-cognizing optimization strategy that prioritizes high-density logical samples to enhance with the LLM's reasoning ability. Extensive experiments demonstrate that our approach enhances reasoning performance and generalization without increasing total data volume. These results, further validated within a reinforcement learning framework, suggest that elevating logical density is more critical than expanding data scale for realizing the full cognitive potential of LLMs. The released code is available in the Appendix C.
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。
