通过残差优化方程，让机器自动改进预测结果
Prompting Neural-Guided Equation Discovery Based on Residuals
- 将初始方程拆解为语法树，按节点计算残差
- 用残差作新目标变量，引导系统生成更优方程
- 兼容各类方程发现系统，无需重新训练
神经引导的方程发现系统利用数据集作为提示，直接预测描述数据的方程，避免了大规模搜索。然而，当预测方程不符合用户预期时，缺乏简便方法获得其他建议，需大量手动调整。为此，我们提出残差方程发现（RED），一种基于残差的后处理方法，可针对性优化已有方程。通过将初始方程解析为语法树，采用基于节点的计算规则，对每个子方程计算残差，并将其作为新目标变量重新构造原始数据集，生成新提示。若在验证集上新建议的子方程表现优于旧方程，则替换之。实验在Feynman基准的53个方程上验证，RED不仅提升所有测试的神经引导系统性能，也改善所有测试的经典遗传编程系统。
原文摘要 · Abstract (English)
Neural-guided equation discovery systems use a data set as prompt and predict an equation that describes the data set without extensive search. However, if the equation does not meet the user's expectations, there are few options for getting other equation suggestions without intensive work with the system. To fill this gap, we propose Residuals for Equation Discovery (RED), a post-processing method that improves a given equation in a targeted manner, based on its residuals. By parsing the initial equation to a syntax tree, we can use node-based calculation rules to compute the residual for each subequation of the initial equation. It is then possible to use this residual as new target variable in the original data set and generate a new prompt. If, with the new prompt, the equation discovery system suggests a subequation better than the old subequation on a validation set, we replace the latter by the former. RED is usable with any equation discovery system, is fast to calculate, and is easy to extend for new mathematical operations. In experiments on 53 equations from the Feynman benchmark, we show that it not only helps to improve all tested neural-guided systems, but also all tested classical genetic programming systems.
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