RASR-94M-M

RASR (Reinforced Amortized Symbolic Regression) is a transformer trained for symbolic regression. Given a numeric dataset (X, y), it samples candidate closed-form expressions, refines their constants numerically, and returns the Pareto front of fit against expression size, without any per-dataset training.

This variant was post-trained with expression-size penalty λ = 0.15. It trades a little fit for smaller expressions than the default RASR-94M-L.

• Paper: Improving Neural Symbolic Regression with a Diverse Prior and Post-training Alignment
• Code: github.com/automl/rasr

Variants

Model	Size penalty λ	Description
RASR-94M-L	0.05	Default, best fit
RASR-94M-M	0.15	Smaller expressions, slightly lower fit
RASR-94M-S	0.5	Smallest expressions
RASR-94M-base	n/a	Pre-trained only, no post-training

Usage

Install the RASR code from github.com/automl/rasr. The weights are downloaded automatically on first use:

from src.rasr.inference.rasr import RASR

model = RASR(model_path="davidotte/RASR-94M-M")
model.fit(X, y)
print(model.get_expression())
y_pred = model.predict(X)

for c in model.pareto_front_:  # Candidates not beaten on both fit and size.
    print(c.complexity, c.r2, c.expression_string)

Uses a GPU if one is available. On a CPU, pass a smaller num_candidates (default 256) for faster fits. Inputs must be numeric without missing values, with at most 11 features.

Model details

• Architecture: Encoder-decoder transformer with 94M parameters. The encoder alternates attention over rows and features, and the decoder generates expressions in prefix notation.
• Operators: +, *, /, pow2–pow5, pow1_2–pow1_5, abs, inv, sin, cos, tanh, exp, log.
• Pre-training: Supervised on ~62M fully synthetic datasets, with inputs drawn from the TabICLv2 prior, data-conditioned constants and heteroscedastic or structured noise.
• Post-training: Risk-sensitive GRPO, rewarding held-out fit after constant refinement and penalizing expression size with λ = 0.15.

Results

Benchmark	RASR-94M-M
SRBench 2.0 black-box track (12 datasets)	On the accuracy-complexity Pareto front. Mean size 18.3 nodes, mean fitting time 69 s

See the paper for the full evaluation.

Citation

If you use RASR in your work, please cite:

@misc{otte2026improvingneuralsymbolic,
  title         = {Improving Neural Symbolic Regression with a Diverse Prior and Post-training Alignment},
  author        = {David Otte and J{\"o}rg K.H. Franke and Frank Hutter},
  year          = {2026},
  eprint        = {2610.17994},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG},
  url           = {https://arxiv.org/abs/2610.17994}
}