# MOSAIC-SR: Transformer-Guided Symbolic Regression for Scientific Equation Recovery

arXiv: https://arxiv.org/abs/2609.20997 · HTML: https://mlsanity.com/paper/2609.20997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 17 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)
- [A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data](https://mlsanity.com/paper/2309.13705/) (2023)

## Abstract (arXiv)

Symbolic regression aims to recover closed-form equations from observations, providing interpretable models for scientific discovery. Existing approaches struggle to combine flexible structural search with efficient inference. Search-based methods can refine expression structure but often rely on costly combinatorial optimization with random initialization. Pretrained neural models generate formulas almost instantly, but their predictions often contain symbolic errors. We introduce MOSAIC-SR, which uses a pretrained Transformer to propose multiple initial sketches. These sketches initialize searches in several promising regions, avoiding random starts in the vast expression space. Each search jointly recovers structure and constants through scale-aware constant optimization and local symbolic repair. We evaluate MOSAIC-SR on the SRSD-Feynman dataset with and without dummy variables and on six additional benchmarks. MOSAIC-SR obtains the highest symbolic solution rate on every dataset while ranking among the top two methods in predictive accuracy. This advantage persists in the presence of irrelevant dummy inputs. The results show that learned priors can focus search on promising equation structures, and that numerical optimization and symbolic repair are important for recovery.