arXiv：cs.LG（机器学习，全量分类）· Mansooreh Montazerin, Antonio Ortega, Ajitesh Srivastava·· 17 小时前AI 评分36
SMILE：统一连续优化与离散符号恢复的符号回归框架
SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery
AI 导读
SMILE 是一个混合符号回归框架，通过结构分析、连续优化和符号恢复三阶段，将连续梯度优化与离散符号恢复统一起来。该框架在 SRBench 的 ground-truth 与黑盒数据集上，于最大噪声水平下取得最高符号解率，并在精度与复杂度之间持续位于 Pareto 前沿，以更短时间恢复出显著更简单的表达式。该工作已被 NeurIPS 2026 接收。
正文
Abstract:Symbolic regression (SR) discovers closed-form mathematical expressions from data, offering interpretability beyond black-box models. Existing methods suffer from slow convergence in combinatorial search spaces and lack mechanisms to exploit compositional structure in the data. We introduce SMILE (Sine, Multiplication, Identity, Logarithm, Exponential), a hybrid framework that unifies continuous gradient-based optimization with discrete symbolic recovery through three stages: structural analysis of the data to identify the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network that encodes the target expression using interpretable activations, and symbolic recovery through structured pruning, coefficient optimization, and rounding. This final stage distills the learned network into a compact expression with exact symbolic constants. We evaluate SMILE on SRBench across ground-truth and black-box datasets, with ablation studies validating each component. SMILE achieves the highest symbolic solution rate at the largest noise levels, demonstrating strong robustness where competing methods degrade substantially. It consistently lies on the Pareto front of accuracy versus complexity, recovering significantly simpler expressions in a fraction of the time required by the competing methods.
| Comments: | Accepted to NeurIPS 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.04639 [cs.LG] |
| (or arXiv:2609.04639v3 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.04639 arXiv-issued DOI via DataCite |
Submission history
From: Mansooreh Montazerin [view email]
[v1]
Fri, 4 Sep 2026 02:20:00 UTC (1,715 KB)
[v2]
Tue, 29 Sep 2026 00:05:27 UTC (1,715 KB)
[v3]
Thu, 1 Oct 2026 01:03:37 UTC (1,715 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org