The paper presents a probabilistic symbolic regression framework that models mathematical expressions as ensembles of symbolic trees, using a regularizing prior to control complexity and an Occam’s window-based posterior to capture uncertainty across plausible models. It provides theoretical guarantees on posterior concentration, including near‑parametric rates when an exact finite formula exists and oracle results under misspecification. Empirical results show the method outperforms state‑of‑the‑art competitors in predictive accuracy, symbolic complexity, and structural recovery on benchmark scientific equations and a materials discovery task.
By Somjit Roy, Pritam Dey, Bani K. Mallick, Debdeep Pati
arXiv:2609.36187v1 Announce Type: new
Abstract: Symbolic Regression (SR) is a data-driven method for scientific discovery which searches for interpretable analytical relationships within data. Recent...
By Cristina Rossetti, Anna V. Kononova, Thomas B\"ack, Fei Liu, Niki Van Stein
arXiv:2606. 09276v1 Announce Type: new Abstract: Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data.
By Paul Kahlmeyer, Henrik Voigt, Michael Habeck, Joachim Giesen
arXiv:2605. 23272v2 Announce Type: replace-cross Abstract: Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data.
By Boxiao Wang, Kai Li, Zhiwei Chen, Yang Huang, Runxiang Wang, Ziwen Zhang, Yifan Zhang, Jian Cheng
arXiv:2606. 07704v1 Announce Type: cross Abstract: Symbolic regression aims to uncover explicit scientific laws from data.
By Zeyu Xia, Jun Zhu, Dong Yan
MOSAIC‑SR is a new symbolic regression method that combines a pretrained Transformer with search‑based refinement. The Transformer generates multiple initial sketches, which seed searches that jointly recover equation structure and constants using scale‑aware optimization and symbolic repair. On the SRSD‑Feynman dataset and six other benchmarks, MOSAIC‑SR achieves the highest symbolic solution rate and ranks among the top two in predictive accuracy, even when irrelevant dummy variables are present.
By Peiyi Zheng, Yanming Kang, Hans De Sterck, Giang Tran