An AI system designed to search for explicit equations recovered 95% of target formulas exactly on the 100-problem Feynman benchmark, with an average R2 of 0.9999, according to an arXiv preprint dated 26 August 2026. Here, exact recovery means the discovered expression was symbolically equivalent to the benchmark’s ground-truth equation.
How the equation search is organized
Symbolic regression here means searching for an explicit expression whose fit is measured against data. The stated objective combines mean squared error with a parsimony penalty tied to expression-tree complexity, so the reported search weighs numerical fit and formula size together.
The method, InsightSR, places a large language model (LLM) layer around PySR. One pathway uses semantic seeds, while the other applies structural feature transformations that accumulate over generations.
After each generation, the LLM evaluates candidate expressions for numerical accuracy, physical interpretability and feature utility, then updates a knowledge base used by both pathways in later iterations. Guidance is therefore carried forward from one generation to the next.
Where the reported scores stood
The evaluation spans three groups: 100 Feynman problems, 240 LLM-SRBench problems and four real-world datasets. The real-world results are reported separately for in-distribution (ID) and out-of-distribution (OOD) data.
To judge the equations, the paper reports R2, NMSE—defined as 1 − R2—Accτ and exact recovery based on symbolic equivalence to the ground truth. These measures keep numerical fit and symbolic identity as separate reported outcomes.
On the LSR-Transform portion of LLM-SRBench, InsightSR’s Acc0.1 was 80.18%, compared with 50.45% for LaSR, the previous best reported system.
Accuracy varied across the named scientific areas: 66.67% in Chemistry, 50.00% in Biology, 40.91% in Physics and 92.00% in Material Science. Material Science was the highest of those four reported figures, while Physics was the lowest.
Across the five LLM-SRBench columns, the reported system NMSE values were 1.3e-14, 8.0e-7, 7.3e-7, 1.6e-5 and 4.7e-8.
The tests also looked beyond the physics set
For the four real-world datasets, the reported in-distribution (ID)/out-of-distribution (OOD) NMSE pairs were 9.55e-11/1.15e-04 for Oscillator 1, 2.45e-09/1.03e-05 for Oscillator 2, 1.76e-03/1.41e-02 for E. coli and 2.00e-02/5.32e-02 for Stress-Strain, respectively.
In every pair, the OOD figure was higher than the ID figure.
A separate Feynman noise test reported Acc0.1 values of 37% at noise 0.05, 68% at 0.01, 72% at 0.005 and 79% at 0.001; with no noise, the score was 97%. The score was lower at each nonzero noise level than at noise 0.
A search built around fit and simplicity
The reported setup used Qwen-3.5 27B at temperature 0.3, 100–500 PySR iterations and 3–30 LLM generations. It used 30 populations of 50 individuals, a parsimony setting of 0.003, a maximum expression size of 20–25 nodes and an early-stop threshold of 10−10.
The caveat around metadata
The main caveat concerns the information supplied at the start. The authors identify initial textual metadata and ambiguous variable semantics as potential sensitivity points for unit synthesis, a concern that sits close to the method’s semantic pathway.
The document is labeled arXiv:2608.25291v1 [cs.LG] and dated 26 Aug 2026, so the results are presented as preprint benchmark evidence.
Paper data and sources
Original title: InsightSR: Refining Symbolic Regression Search Spaces via Parallel Semantic and Structural LLM Guidance
Authors: Yating Ling, Wenjing Cun, Zhitang Chen
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text