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
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
arXiv:2511. 04124v3 Announce Type: replace Abstract: Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data.
By Giorgio Morales, John W. Sheppard
arXiv:2607. 21855v1 Announce Type: new Abstract: We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks.
By Charles Brum, Edward Finkelstein
arXiv:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
By Ethan Smith
arXiv:2605. 23272v2 Announce Type: replace-cross Abstract: Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data.
By Boxiao Wang, Kai Li, Zhiwei Chen, Yang Huang, Runxiang Wang, Ziwen Zhang, Yifan Zhang, Jian Cheng
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
Biologically-informed neural networks (BINNs) are a subclass of physics-informed neural networks tailored for learning partial differential equations in biological systems, where equations are nonlinear and data are sparse. The paper introduces a diagnostic workflow for selecting hyperparameters—network capacity, training epochs, and term stability—without requiring known ground-truth equations. By applying this workflow to synthetic systems, the authors show that validation loss tracks true error and provide practical guidelines and starting values for BINN hyperparameter tuning.
By William Lavery, Jodie A. Cochrane, John T. Nardini, Sara Hamis
arXiv:2607. 09235v1 Announce Type: cross Abstract: The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability.
By Jayadeva, Madhur Aswani
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
arXiv:2606. 09276v1 Announce Type: new Abstract: Equation discovery aims to automate the discovery of scientific models in the form of mathematical equations from data.
By Paul Kahlmeyer, Henrik Voigt, Michael Habeck, Joachim Giesen
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