REVIEW 14 cited by
Contemporary Symbolic Regression Methods and their Relative Performance
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this shortcoming by introducing an open-source, reproducible benchmarking platform for symbolic regression. We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. Our assessment includes both real-world datasets with no known model form as well as ground-truth benchmark problems, including physics equations and systems of ordinary differential equations. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity relative to state-of-the-art machine learning methods. For the synthetic problems, we assess each method's ability to find exact solutions in the presence of varying levels of noise. Under these controlled experiments, we conclude that the best performing methods for real-world regression combine genetic algorithms with parameter estimation and/or semantic search drivers. When tasked with recovering exact equations in the presence of noise, we find that deep learning and genetic algorithm-based approaches perform similarly. We provide a detailed guide to reproducing this experiment and contributing new methods, and encourage other researchers to collaborate with us on a common and living symbolic regression benchmark.
Forward citations
Cited by 14 Pith papers
-
NestyNet. I. Physics Functions Are Hard to Fit with Neural Networks: A Framework for Accurate Surrogates and Analytic Derivatives
NestyNet, a segmented softplus model with analytic derivatives and a second-order optimizer, reports 2,100x better function values and 1,400x better derivatives than Adam-trained MLPs on AI Feynman.
-
A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordination
A-SR is an agentic LLM framework that improves symbolic regression success rates through role-conditioned evidence routing, protocol selection, and online role-policy adaptation.
-
Data-Efficient Symbolic Regression via Foundation Model Distillation
EQUATE fine-tunes a pre-trained symbolic regression transformer with symbolic-numeric alignment and evaluator-guided embedding search, outperforming its backbone and most baselines on Feynman, Strogatz, and black-box ...
-
Fast Symbolic Regression Benchmarking
A curated-list plus early-termination protocol for symbolic regression benchmarks raises measured rediscovery rates and cuts benchmark compute by roughly half.
-
Diffusion-Based Symbolic Regression
A masked discrete diffusion model trained with token-wise GRPO and a long short-term risk-seeking replay pool improves symbolic regression solution rates and expression simplicity on SRBench.
-
Bridging the Domain Gap in Equation Distillation with Reinforcement Feedback
Reinforcement learning fine-tuning with numerical fitness rewards improves equation discovery accuracy and noise robustness of a pretrained symbolic regression transformer.
-
Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks
Vision-capable LLMs can propose useful function forms from plots alone, and combining this with KANs gives a viable route to multivariate symbolic regression.
-
Thinking Outside the Template with Modular GP-GOMEA
Modular GP-GOMEA, which evolves multiple tree templates that can hierarchically call each other as subexpressions, generally beats single-template GP-GOMEA in accuracy on tested benchmarks and recovers modular ground-...
-
Machine Learning-Based Analytical Expressions for Gray-Body Factors and Application to Primordial Black Holes
Symbolic regression is used to derive compact error-function approximations for Schwarzschild gray-body factors, and the approximations reproduce the Hawking spectra and primordial black hole constraints from full num...
-
Exploring Multi-view Symbolic Regression methods in physical sciences
Benchmarking four multi-view symbolic regression packages on five real scientific datasets shows all find accurate compact models; parameter limits and shared constants emerge as key design features.
-
AutoSciLab: A Self-Driving Laboratory For Interpretable Scientific Discovery
AutoSciLab combines generative modeling, active learning, and symbolic regression into one loop, but its headline nanophotonics discovery is validated only on a neural-network surrogate and its Ising rediscovery presu...
-
Knowledge-based model validation using a custom metric
A custom validation metric is built by regressing expert face-validation ratings on standard time-series error features, with prediction intervals reported for the resulting score.
-
SymbolFit: Automatic Parametric Modeling with Symbolic Regression
Symbolic regression with a re-optimization step automates parametric modeling of binned high-energy physics data and provides uncertainty estimates.
-
(Exhaustive) Symbolic Regression and model selection by minimum description length
Exhaustive search over simple functions ranked by description length beats the Friedmann equation, MOND, and common inflaton potentials on astrophysical datasets.
Discussion (0). Continue with ORCID to comment.