Symbolic regression (SR) aims to discover interpretable analytical expressions that accurately describe observed data. Amortized SR promises to be much more efficient than the predominant genetic programming SR methods, but currently struggles to scale to realistic scientific complexity. We find that a key obstacle is the lack of a fast reduction of equivalent expressions to a concise normalized form. Amortized SR has addressed this by general-purpose Computer Algebra Systems (CAS) like SymPy, but the high computational cost severely limits training and inference speed. We propose SimpliPy, a rule-based simplification engine achieving a 100-fold speed-up over SymPy at comparable quality. This enables substantial improvements in amortized SR, including scalability to much larger training sets, more efficient use of the per-expression token budget, and systematic training set decontamination with respect to equivalent test expressions. We demonstrate these advantages in our Flash-ANSR framework, which achieves much better accuracy than amortized baselines (NeSymReS, E2E) on the FastSRB benchmark. Moreover, it performs on par with state-of-the-art direct optimization (PySR) while recovering more concise instead of more complex expressions with increasing inference budget.

翻译：符号回归（SR）旨在发现可解释的解析表达式，以准确描述观测数据。摊销式符号回归有望比主流的遗传编程符号回归方法高效得多，但目前难以扩展到现实科学问题的复杂度。我们发现一个关键障碍在于缺乏将等价表达式快速约简为简洁规范形式的方法。摊销式符号回归已通过通用计算机代数系统（如SymPy）处理此问题，但高昂的计算成本严重限制了训练和推理速度。我们提出SimpliPy，一种基于规则的简化引擎，在质量相当的情况下比SymPy实现100倍的加速。这为摊销式符号回归带来了实质性改进，包括扩展到更大的训练集、更高效地利用每个表达式的标记预算，以及针对等价测试表达式进行系统化的训练集去污染。我们在Flash-ANSR框架中展示了这些优势，该框架在FastSRB基准测试上取得了比摊销式基线方法（NeSymReS、E2E）好得多的准确性。此外，其性能与最先进的直接优化方法（PySR）相当，同时随着推理预算的增加能恢复更简洁而非更复杂的表达式。