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This research introduces a Neural Symbolic Regression (NSR) framework that leverages neural networks as preconditioners to enhance the scalability and noise robustness of symbolic discovery. By decoupling smooth approximation from sparse expression extraction via LASSO, the method achieves superior performance on benchmark suites compared to traditional Genetic Programming and SINDy approaches. The work effectively bridges deep learning approximation with interpretable scientific machine learning, addressing key limitations in current feature library dependencies.
Neural Symbollic Regression Using Deep Learning and Sparse Modelling
arXiv:2609.01102v1 Announce Type: cross Abstract: Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.
Abstract:Symbolic Regression (SR) seeks to find succinct mathematical expressions that represent the fundamental relationships within data, providing interpretability and scientific understanding that exceeds that of black-box models. Nevertheless, traditional methods like Genetic Programming face challenges with scalability and are highly sensitive to noise, while sparse regression techniques such as SINDy rely significantly on predetermined feature libraries. In this work, we present a Neural Symbolic Regression (NSR) framework that treats neural networks as functional preconditioners for symbolic discovery. Our approach uses a decoupled pipeline: a neural network first learns a smooth, noise-robust approximation of the target function in an interaction- aware nonlinear feature space. LASSO is then applied to extract sparse, interpretable closed-form expressions. To improve predictive accuracy and symbolic fidelity by integrating distributed hyperparameter optimization with Ray Tune and ASHA scheduling. Experiments on the Nguyen benchmark suite show that our approach consistently outperforms SINDy and non-tuned neural baselines in RMSE, noise robustness, and out-of-distribution generalization. Ablation studies confirm the significance of feature interactions, neural depth, and tuning strategies. In general, this study presents a scalable and understandable neural-symbolic framework, creating a solid link between neural approximation and the discovery of sparse equations for scientific machine learning.
Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE); Symbolic Computation (cs.SC)
arXiv:2609.01102 [cs.LG]
(or arXiv:2609.01102v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.01102 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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