LLM-SR
An LLM proposes equation shapes as Python functions, an optimizer fits their constants to data, and the scores steer later proposals.
The loop
- Proposes
Equation skeletons as Python functions with placeholder parameters
- Judged by
Fitting parameters with BFGS or Adam and scoring negative mean squared error against data
- Steers
An experience buffer of 10 islands feeds the best equations (k=2) into the next prompt
Headline result
Across four problems (two oscillators, E. coli growth, aluminum stress-strain) with about 2.5K iterations, LLM-SR beat symbolic regression baselines on normalized MSE, most clearly out of domain: for E. coli growth 0.0037 against 1.0141 for the best baseline.
What this does not prove
Four benchmarks, two of them custom-built. Baselines (e.g. PySR) ran with far more evaluations (2M+). Results use GPT-3.5-turbo or Mixtral-8x7B; the best model differs by problem.
How it generalizes the harness
The island-based search with data fitting is the solver, and the discovered equation is a compact scientific artifact usable without the LLM.
Classification
| What it proposes | Equation |
|---|---|
| Generative model | Frozen LLM (GPT-3.5-turbo, Mixtral-8x7B) |
| Algorithmic authority | Numerical fit to data scored by error |
| Feedback | Score |
| What gets updated | Prompt context and population of candidates |
| When it runs | At inference time |
| Validity | Empirical (measured) |
| Evidence | Experiments reported |
| Lineage | Derivative |