arXiv:2505.12440cs.AI2025-05

用语法演化生成可读的数学模型,探索质数规律。

Model Discovery with Grammatical Evolution. An Experiment with Prime Numbers

  • 用语法演化自动构造数学公式形式的解析模型。
  • 成功发现描述质数分布的简洁数学表达式。
  • 适合对可解释性建模感兴趣的科研人员。

机器学习仅根据输入输出数据构建高效决策与预测模型,如决策树或神经网络,但缺乏透明性。而基于数学公式的解析模型具有可解释、简洁和结构清晰的优点,其发现需额外知识,可通过语法演化实现。本文报告了一项非平凡实验,利用语法演化生成描述质数分布的解析模型,验证了该方法在复杂数学规律发现中的可行性与有效性。

原文摘要 · Abstract (English)

Machine Learning produces efficient decision and prediction models based on input-output data only. Such models have the form of decision trees or neural nets and are far from transparent analytical models, based on mathematical formulas. Analytical model discovery requires additional knowledge and may be performed with Grammatical Evolution. Such models are transparent, concise, and have readable components and structure. This paper reports on a non-trivial experiment with generating such models.

模型发现语法演化可解释性

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