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arXiv Machine Learning

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.

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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
Sep 7

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.

By Mansooreh Montazerin, Antonio Ortega, Ajitesh Srivastava
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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 Machine Learning
Sep 21

MOSAIC-SR: Transformer-Guided Symbolic Regression for Scientific Equation Recovery

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
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arXiv Machine Learning
Oct 15

Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression

The paper introduces an exhaustive dataset of univariate canonical skeletons for neural symbolic regression, generated deterministically via a constrained context-free grammar. These skeletons serve as generic structural representations that eliminate redundant expressions and provide uniform operator distribution, thereby avoiding simplicity bias. The authors also present a sampling strategy for clean numerical data and benchmark 150 SR problems across three tiers, demonstrating challenges for current state‑of‑the‑art methods.

By Giorgio Morales, Anik\'o Ek\'art
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arXiv AI
Oct 2

Auto-Formalizing Neuro-Symbolic Predictors

arXiv:2610.01519v1 Announce Type: cross Abstract: Neuro-Symbolic (NeSy) predictors incorporate prior knowledge into the prediction process of neural networks, ensuring that outputs satisfy specified...

By Samuele Bortolotti, Weixin Chen, Han Zhao, Andrea Passerini, Stefano Teso, Antonio Vergari
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arXiv Statistics ML
Oct 26

Softly Symbolifying Kolmogorov-Arnold Networks

Softly Symbolified Kolmogorov–Arnold Networks (S2KAN) integrate symbolic primitives into the training of Kolmogorov–Arnold Networks, allowing each activation to be expressed as a sparse combination of symbolic and dense terms. The sparsification is differentiable and guided by a minimum description length–inspired objective, enabling end‑to‑end optimization. Across real‑world prediction tasks, dynamical‑system forecasting, and synthetic symbolic benchmarks, S2KAN achieves higher symbolic fidelity, often with smaller models while maintaining competitive predictive accuracy.

By James Bagrow, Josh Bongard
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