LaSR
Library-Augmented Symbolic Regression
Interleaves genetic programming and BFGS constant optimization (PySR) with LLM-synthesized abstract concept libraries for equation discovery.
The loop
- Proposes
An LLM abstracts recurring sub-expressions from top equations into reusable symbolic concepts and seeds mutated expression trees.
- Judged by
A high-performance symbolic regression engine (PySR) optimizes numerical constants via BFGS and scores MSE accuracy and complexity on scientific datasets.
- Steers
Tournament selection and Pareto-front complexity filtering retain the fittest symbolic equations and evolve the concept library.
Headline result
Recovered significantly more exact ground-truth physical laws on the Feynman Symbolic Regression Benchmark than standalone PySR or LLM-only baselines.
What this does not prove
Calling an LLM inside evolutionary epochs increases wall-clock runtime compared to pure Julia genetic programming.
How it generalizes the harness
- The algorithm is the solver
- Inverted control
- The output outlives the model
- Search over a population
- Continuous-discrete duality
The PySR evolutionary + BFGS numerical optimizer runs the population loop and queries the LLM to evolve abstract symbolic building blocks.
Classification
| What it proposes | Equation |
|---|---|
| Generative model | LLM symbolic concept and mutation generator |
| Algorithmic authority | PySR genetic programming and BFGS numerical optimizer |
| Feedback | Score |
| What gets updated | Population of candidates and prompt context |
| When it runs | Offline, at design time |
| Validity | Empirical (measured) |
| Evidence | Code released |
| Lineage | Original system |