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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

Deep learning provides a promising way to extract effective representations from raw data in an end-to-end fashion and has proven its effectiveness in various domains such as computer vision, natural language processing, etc. However, in…

Machine Learning · Computer Science 2021-07-06 Hui Li , Xing Fu , Ruofan Wu , Jinyu Xu , Kai Xiao , Xiaofu Chang , Weiqiang Wang , Shuai Chen , Leilei Shi , Tao Xiong , Yuan Qi

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

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Machine Learning · Computer Science 2023-03-17 Mengge Du , Yuntian Chen , Dongxiao Zhang

Recent progress in deep reinforcement learning (DRL) can be largely attributed to the use of neural networks. However, this black-box approach fails to explain the learned policy in a human understandable way. To address this challenge and…

Artificial Intelligence · Computer Science 2021-03-17 Zhihao Ma , Yuzheng Zhuang , Paul Weng , Hankz Hankui Zhuo , Dong Li , Wulong Liu , Jianye Hao

Deep Reinforcement Learning (DRL) algorithms often require a large amount of data and struggle in sparse-reward domains with long planning horizons and multiple sub-goals. In this paper, we propose a neuro-symbolic extension of Proximal…

Artificial Intelligence · Computer Science 2026-04-29 Simone Murari , Celeste Veronese , Daniele Meli

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

Optimization and Control · Mathematics 2024-01-04 Daokuan Zhu , Tianqi Xu , Jie Lu

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve…

Machine Learning · Computer Science 2022-07-06 Brenden K. Petersen , Mikel Landajuela , T. Nathan Mundhenk , Claudio P. Santiago , Soo K. Kim , Joanne T. Kim

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives…

Machine Learning · Computer Science 2024-01-08 Kevin Black , Michael Janner , Yilun Du , Ilya Kostrikov , Sergey Levine

Continual learning aims to learn multiple tasks sequentially while preserving prior knowledge, but faces the challenge of catastrophic forgetting when adapting to new tasks. Recently, approaches leveraging pre-trained models have gained…

Computer Vision and Pattern Recognition · Computer Science 2025-11-12 Quan Cheng , Yuanyu Wan , Lingyu Wu , Chenping Hou , Lijun Zhang

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

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

Neural and Evolutionary Computing · Computer Science 2017-03-23 Shumeet Baluja

Symbolic Regression (SR) enables the discovery of interpretable mathematical relationships from experimental and simulation data. These relationships are often coined descriptors which are defined as a fundamental materials property that is…

Computational Physics · Physics 2026-02-10 Udaykumar Gajera , Mohsen Sotoudeh , Kanchan Sarkar , Axel Groß

Learning options that allow agents to exhibit temporally higher order behavior has proven to be useful in increasing exploration, reducing sample complexity and for various transfer scenarios. Deep Discovery of Options (DDO) is a generative…

Machine Learning · Computer Science 2019-08-06 Ameet Deshpande , Harshavardhan Kamarthi , Balaraman Ravindran

Symbolic regression (SR) aims to discover mathematical expressions from data, a task traditionally tackled using Genetic Programming (GP) through combinatorial search over symbolic structures. Latent Space Optimization (LSO) methods use…

Neural and Evolutionary Computing · Computer Science 2026-04-14 Benjamin Léger , Kazem Meidani , Christian Gagné

Most reinforcement learning algorithms seek a single optimal strategy that solves a given task. However, it can often be valuable to learn a diverse set of solutions, for instance, to make an agent's interaction with users more engaging, or…

Machine Learning · Computer Science 2024-01-09 Wentse Chen , Shiyu Huang , Yuan Chiang , Tim Pearce , Wei-Wei Tu , Ting Chen , Jun Zhu

Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…

Computation and Language · Computer Science 2018-01-12 Paul Tupper , Paul Smolensky , Pyeong Whan Cho

Symbolic Regression (SR) is a regression method that aims to discover mathematical expressions that describe the relationship between variables, and it is often implemented through Genetic Programming, a metaphor for the process of…

Neural and Evolutionary Computing · Computer Science 2025-12-02 Guilherme Seidyo Imai Aldeia

Recent studies on Learning to Optimize (L2O) suggest a promising path to automating and accelerating the optimization procedure for complicated tasks. Existing L2O models parameterize optimization rules by neural networks, and learn those…

Machine Learning · Computer Science 2022-05-10 Wenqing Zheng , Tianlong Chen , Ting-Kuei Hu , Zhangyang Wang

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