Saved in:
| Main Authors: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.13021 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911449504284672 |
|---|---|
| author | Xiao, Jing Chen, Xinhai Peng, Jiaming Wang, Qinglin Jia, Menghan Lai, Zhiquan Yu, Guangping Li, Dongsheng Li, Tiejun Liu, Jie |
| author_facet | Xiao, Jing Chen, Xinhai Peng, Jiaming Wang, Qinglin Jia, Menghan Lai, Zhiquan Yu, Guangping Li, Dongsheng Li, Tiejun Liu, Jie |
| contents | Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery Xiao, Jing Chen, Xinhai Peng, Jiaming Wang, Qinglin Jia, Menghan Lai, Zhiquan Yu, Guangping Li, Dongsheng Li, Tiejun Liu, Jie Machine Learning Artificial Intelligence Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap: producing equations that fit observations well but remain inconsistent with fundamental scientific principles. A key reason is that these approaches are dominated by empirical risk minimization, lacking explicit constraints to ensure scientific consistency. To bridge this gap, we propose PG-SR, a prior-guided SR framework built upon a three-stage pipeline consisting of warm-up, evolution, and refinement. Throughout the pipeline, PG-SR introduces a prior constraint checker that explicitly encodes domain priors as executable constraint programs, and employs a Prior Annealing Constrained Evaluation (PACE) mechanism during the evolution stage to progressively steer discovery toward scientifically consistent regions. Theoretically, we prove that PG-SR reduces the Rademacher complexity of the hypothesis space, yielding tighter generalization bounds and establishing a guarantee against pseudo-equations. Experimentally, PG-SR outperforms state-of-the-art baselines across diverse domains, maintaining robustness to varying prior quality, noisy data, and data scarcity. |
| title | Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discovery |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.13021 |