发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
MOSAIC-SR利用预训练Transformer生成初始草图，引导符号回归搜索，通过尺度感知常数优化和局部符号修复，在多个基准上实现最高符号解率与高预测精度。
AI 中文摘要
符号回归旨在从观测中恢复封闭形式的方程，为科学发现提供可解释的模型。现有方法难以兼顾灵活的结构搜索与高效的推理。基于搜索的方法能够细化表达式结构，但往往依赖于带有随机初始化的昂贵组合优化。预训练的神经模型几乎能即时生成公式，但其预测常包含符号错误。我们提出了MOSAIC-SR，该方法利用预训练的Transformer来提出多个初始草图。这些草图在多个有前景的区域初始化搜索，避免了在庞大的表达式空间中进行随机启动。每次搜索通过尺度感知的常数优化和局部符号修复，联合恢复结构和常数。我们在SRSD-Feynman数据集上（含和不含虚拟变量）以及六个额外基准上评估了MOSAIC-SR。MOSAIC-SR在每个数据集上都获得了最高的符号解率，同时在预测准确性方面排名前两位。这一优势在存在无关虚拟输入时依然保持。结果表明，学习到的先验可以将搜索聚焦于有前景的方程结构，并且数值优化和符号修复对于恢复至关重要。
英文摘要
Symbolic regression aims to recover closed-form equations from observations, providing interpretable models for scientific discovery. Existing approaches struggle to combine flexible structural search with efficient inference. Search-based methods can refine expression structure but often rely on costly combinatorial optimization with random initialization. Pretrained neural models generate formulas almost instantly, but their predictions often contain symbolic errors. We introduce MOSAIC-SR, which uses a pretrained Transformer to propose multiple initial sketches. These sketches initialize searches in several promising regions, avoiding random starts in the vast expression space. Each search jointly recovers structure and constants through scale-aware constant optimization and local symbolic repair. We evaluate MOSAIC-SR on the SRSD-Feynman dataset with and without dummy variables and on six additional benchmarks. MOSAIC-SR obtains the highest symbolic solution rate on every dataset while ranking among the top two methods in predictive accuracy. This advantage persists in the presence of irrelevant dummy inputs. The results show that learned priors can focus search on promising equation structures, and that numerical optimization and symbolic repair are important for recovery.
