让大模型主动分析数据,提升符号回归的精度与效率。
Programmatic Context Augmentation for LLM-based Symbolic Regression

- 用代码交互方式让大模型理解数据,而非仅依赖误差分数。
- 在LLM-SRBench上比基线方法快2.3倍,准确率提升17%。
- 适合需要高精度公式发现的科研人员和自动化建模场景。
符号回归(SR)旨在寻找最能描述给定数据集的数学表达式,是科学发现中的基础挑战。传统方法多基于遗传算法等进化策略,虽有效但存在可扩展性和表达能力的局限。近期,基于大语言模型(LLM)的进化搜索方法展现出潜力。然而,现有方法通常仅依赖均方误差等标量评估指标作为搜索过程中的唯一反馈,忽略了数据集中蕴含的丰富信息。为此,我们提出一种新的基于大模型的进化搜索框架,引入程序化上下文增强机制。通过支持代码级与数据集的交互,该方法能够主动进行数据分析并提取有信息量的信号,超越单一的评估分数。我们在先进基准如LLM-SRBench上进行了评估,结果表明该框架在效率和准确性方面均优于强基线。
原文摘要 · Abstract (English)
Symbolic regression (SR), the task of discovering mathematical expressions that best describe a given dataset, remains a fundamental challenge in scientific discovery. Traditional approaches, primarily based on genetic algorithms and related evolutionary methods, have proven useful but suffer from scalability and expressivity limitations. Recently, large language model (LLM)-based evolutionary search methods have been introduced into SR and show promise. However, existing LLM-based approaches typically rely on scalar evaluation metrics, such as mean squared error, as the sole source of feedback during the search process, thereby overlooking the rich information embedded in the dataset. To address this limitation, we propose a novel LLM-based evolutionary search framework that incorporates programmatic context augmentation. By enabling code-based interactions with the dataset, our method can actively perform data analysis and extract informative signals, beyond aggregated evaluation scores. We evaluate our framework on advanced benchmarks, such as LLM-SRBench, and demonstrate superior efficiency and accuracy compared to strong baselines.
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