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Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex…

Machine Learning · Computer Science 2024-01-02 Samuel Holt , Zhaozhi Qian , Mihaela van der Schaar

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

Methodology · Statistics 2020-01-17 Ying Jin , Weilin Fu , Jian Kang , Jiadong Guo , Jian Guo

We propose a novel deep symbolic regression approach to enhance the robustness and interpretability of data-driven mathematical expression discovery. Our work is aligned with the popular DSR framework which focuses on learning a…

Machine Learning · Computer Science 2026-03-30 Zachary Bastiani , Robert M. Kirby , Jacob Hochhalter , Shandian Zhe

This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on…

Machine Learning · Computer Science 2025-01-06 Yoshitomo Matsubara , Naoya Chiba , Ryo Igarashi , Yoshitaka Ushiku

Symbolic regression (SR) has emerged as a pivotal technique for uncovering the intrinsic information within data and enhancing the interpretability of AI models. However, current state-of-the-art (sota) SR methods struggle to perform…

Machine Learning · Computer Science 2025-01-03 Chenglu Sun , Shuo Shen , Wenzhi Tao , Deyi Xue , Zixia Zhou

Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic…

Instrumentation and Methods for Astrophysics · Physics 2023-12-27 Wassim Tenachi , Rodrigo Ibata , Foivos I. Diakogiannis

The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…

Machine Learning · Computer Science 2020-06-15 Vernon Austel , Cristina Cornelio , Sanjeeb Dash , Joao Goncalves , Lior Horesh , Tyler Josephson , Nimrod Megiddo

Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the…

Machine Learning · Computer Science 2025-08-21 Viktor Martinek

Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of…

Machine Learning · Computer Science 2023-05-05 Charles Fox , Neil Tran , Nikki Nacion , Samiha Sharlin , Tyler R. Josephson

Vertical Symbolic Regression (VSR) recently has been proposed to expedite the discovery of symbolic equations with many independent variables from experimental data. VSR reduces the search spaces following the vertical discovery path by…

Machine Learning · Computer Science 2024-02-02 Nan Jiang , Md Nasim , Yexiang Xue

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…

Neural and Evolutionary Computing · Computer Science 2023-04-19 Peng Zeng , Xiaotian Song , Andrew Lensen , Yuwei Ou , Yanan Sun , Mengjie Zhang , Jiancheng Lv

We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset…

Machine Learning · Computer Science 2025-09-15 Marco Andrea Bühler , Gonzalo Guillén-Gosálbez

The high-energy physics community is investigating the potential of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to enhance physics sensitivity while still meeting data processing time constraints. In…

Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…

Machine Learning · Computer Science 2024-07-11 Xieting Chu , Hongjue Zhao , Enze Xu , Hairong Qi , Minghan Chen , Huajie Shao

Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert…

Machine Learning · Computer Science 2024-10-16 Haiquan Qiu , Shuzhi Liu , Quanming Yao

We study the potential of symbolic regression (SR) to derive compact and precise analytic expressions that can improve the accuracy and simplicity of phenomenological analyses at the Large Hadron Collider (LHC). As a benchmark, we apply SR…

High Energy Physics - Phenomenology · Physics 2024-12-12 Manuel Morales-Alvarado , Daniel Conde , Josh Bendavid , Veronica Sanz , Maria Ubiali

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…

Machine Learning · Computer Science 2024-09-20 Yanjie Li , Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Meilan Hao , Su Wei , Yusong Deng

Symbolic regression discovers explicit, interpretable equations without assuming a functional form in advance. A Bayesian approach strengthens this through probability distributions over candidate expressions, thus quantifying uncertainty…

Machine Learning · Computer Science 2026-05-05 James Butterworth , Gevik Grigorian , Alejandro DiazDelaO

Symbolic regression (SR) aims to discover explicit mathematical expressions that explain observed data and is widely used in domains where interpretability is essential. Because interpretability requires expressions to reflect meaningful…

Neural and Evolutionary Computing · Computer Science 2026-05-18 Koki Ikeda , Masahiro Nomura , Ryoki Hamano

Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…

Machine Learning · Computer Science 2025-09-17 Xiaoxu Han , Chengzhen Ning , Jinghui Zhong , Fubiao Yang , Yu Wang , Xin Mu
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