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arXiv Machine Learning

SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery

SMILE (Sine, Multiplication, Identity, Logarithm, Exponential) is a hybrid framework that merges continuous gradient-based optimization with discrete symbolic recovery for symbolic regression. It operates in three stages: structural analysis to uncover the compositional hierarchy of the target expression, continuous optimization to learn parameters of a network using interpretable activations, and symbolic recovery via structured pruning, coefficient optimization, and rounding to produce a compact expression with exact symbolic constants. Evaluated on SRBench, SMILE achieves the highest symbolic solution rate under high noise, remains on the Pareto front of accuracy versus complexity, and recovers simpler expressions much faster than competing methods.

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arXiv Machine Learning
Sep 2

Neural Symbollic Regression Using Deep Learning and Sparse Modelling

Neural Symbolic Regression (NSR) uses neural networks as functional preconditioners to learn smooth, noise‑robust approximations of target functions in an interaction‑aware nonlinear feature space. A subsequent LASSO step extracts sparse, interpretable closed‑form expressions, while distributed hyperparameter optimization with Ray Tune and ASHA scheduling improves predictive accuracy and symbolic fidelity. Experiments on the Nguyen benchmark demonstrate that NSR outperforms SINDy and untuned neural baselines in RMSE, noise robustness, and out‑of‑distribution generalization, with ablation studies highlighting the importance of feature interactions, neural depth, and tuning strategies.

By Ravi Kumar U, Sumitra S
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arXiv Machine Learning
Aug 27

InsightSR: Refining Symbolic Regression Search Spaces via Parallel Semantic and Structural LLM Guidance

InsightSR is a new framework that integrates Large Language Models (LLMs) with the PySR genetic programming engine to refine symbolic regression search spaces. It employs two LLM-guided pathways: a Semantic Seed Pathway that generates dimensionally consistent functional skeletons, and a Structural Feature Pathway that suggests nonlinear feature transformations. Over successive iterations, these pathways expand the input space and shift the search toward shallow, semantically informed trees, with a feedback loop that evaluates and refines candidate features. The method achieves a 95% exact recovery rate on the Feynman benchmark and 80.18% accuracy on the LLM-SRBench LSR-Transform task, outperforming existing genetic programming and neural-symbolic approaches while preserving strong out-of-distribution generalization.

By Yating Ling, Wenjing Cun, Zhitang Chen
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arXiv Machine Learning
Aug 31

Probabilistic Symbolic Regression for Equation Discovery via Operator-induced and Regularized Symbolic Forests

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
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arXiv Machine Learning
Aug 31

SymboLLM-FE: LLM-Accelerated Symbolic Regression for Automated Feature Engineering on Tabular Data

SymboLLM-FE combines symbolic regression and large language models to automate feature engineering for tabular data. It first extracts mathematically expressive formulas that correlate strongly with the target, then refines them with LLMs to improve interpretability. Experiments on six real‑world datasets and four Kaggle competitions show that SymboLLM‑FE outperforms existing AutoFE methods while reducing the number of costly LLM calls.

By Zi-Jian Cheng, Zi-Yi Jia, Zhi Zhou, Yu-Feng Li, Lan-Zhe Guo
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arXiv AI
Jun 9

EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification

arXiv:2606. 07915v1 Announce Type: new Abstract: Neural symbolic regression models improve inference efficiency by shifting structural search to pretraining, but their one-pass autoregressive decoding is prone to error accumulation, which may lead to generating structurally incorrect expressions, especially in complex expression generation scenarios.

By Da Li, Xinxin Li, Xingyu Cui, Jin Xu, Juan Zhang, Junping Yin
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