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.
arXiv:2602. 23561v2 Announce Type: replace-cross Abstract: Symbolic regression (SR) has gained recent traction in AI-driven scientific discovery for learning closed-form physical laws.
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.
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.
arXiv:2608. 09617v1 Announce Type: new Abstract: Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs.
arXiv:2609.36187v1 Announce Type: new Abstract: Symbolic Regression (SR) is a data-driven method for scientific discovery which searches for interpretable analytical relationships within data. Recent...
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.
arXiv:2608. 16876v1 Announce Type: cross Abstract: We introduce Automatic Symbolic Regression (AutoSR), a fully automated system that instantiates Research-Space Symbolic Regression by searching persistent scientific investigations rather than isolated equations.
arXiv:2604. 17402v2 Announce Type: replace Abstract: Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data.
L2G-SR is a framework that enhances large language model (LLM)-based symbolic regression by incorporating a learned structural verifier. The verifier uses tree edit distance (TED) to assess structural similarity between candidate equations and the target, complementing numerical error during search. Experiments on LLM-SRBench show that L2G-SR achieves state‑of‑the‑art performance in numerical fit, equation‑level accuracy, and TED across various LLM backbones and domains.
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.
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.
The paper introduces RISR, a residual‑informed approach for symbolic regression that leverages error patterns to guide formula discovery. A residual encoder transforms aligned inputs, targets, predictions, and residuals into tokens that condition a language model to propose candidate equations, while a dual‑view relational encoder predicts the utility of corrections. Evaluated on the LLM‑SRBench, RISR achieves higher in‑distribution and out‑of‑distribution accuracy than baseline methods, demonstrating that incorporating residual information can improve numerical equation recovery.