Symbolic regression (SR) searches for parametric models that accurately fit a dataset, prioritizing simplicity and interpretability. Despite this secondary objective, studies point out that the models are often overly complex due to redundant operations, introns, and bloat that arise during the iterative process, and can hinder the search with repeated exploration of bloated segments. Applying a fast heuristic algebraic simplification may not fully simplify the expression and exact methods can be infeasible depending on size or complexity of the expressions. We propose a novel agnostic simplification and bloat control for SR employing an efficient memoization with locality-sensitive hashing (LHS). The idea is that expressions and their sub-expressions traversed during the iterative simplification process are stored in a dictionary using LHS, enabling efficient retrieval of similar structures. We iterate through the expression, replacing subtrees with others of same hash if they result in a smaller expression. Empirical results shows that applying this simplification during evolution performs equal or better than without simplification in minimization of error, significantly reducing the number of nonlinear functions. This technique can learn simplification rules that work in general or for a specific problem, and improves convergence while reducing model complexity.

翻译：符号回归（SR）旨在搜索精确拟合数据集的参数化模型，并优先考虑简洁性与可解释性。尽管这一优化目标已明确，但研究表明，迭代过程中产生的冗余操作、内含子及膨胀问题常导致模型过于复杂，且对膨胀片段的重复探索会阻碍搜索效率。快速启发式代数简化可能无法完全简化表达式，而精确方法在处理规模较大或结构复杂的表达式时往往不可行。我们提出一种面向符号回归的新型无关性简化与膨胀控制方法，该方法采用基于局部敏感哈希（LSH）的高效记忆化技术。核心思想是将迭代简化过程中遍历的表达式及其子表达式存入基于LSH的字典，从而实现对相似结构的高效检索。我们遍历表达式，若替换为相同哈希值的子树能获得更简化的表达式，则执行替换操作。实验结果表明，在进化过程中应用该简化方法，其误差最小化效果优于或等同于不进行简化的方法，同时显著减少了非线性函数的数量。该技术可学习通用或特定问题的简化规则，在降低模型复杂度的同时提升收敛速度。