# SymMatika: Structure-Aware Symbolic Discovery

arXiv: https://arxiv.org/abs/2507.03110 · HTML: https://mlsanity.com/paper/2507.03110/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [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)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Self-Adjusting Mutation Rates with Provably Optimal Success Rules](https://mlsanity.com/paper/1902.02588/) (2019)
- [Noise-Resilient Symbolic Regression with Dynamic Gating Reinforcement Learning](https://mlsanity.com/paper/2501.01085/) (2025)

## Abstract (arXiv)

Symbolic regression (SR) seeks to recover closed-form mathematical expressions that describe observed data. While existing methods have advanced the discovery of either explicit mappings (i.e., y = f(x)) or discovering implicit relations (i.e., F(x, y)=0), few modern and accessible frameworks support both. Moreover, most approaches treat each expression candidate in isolation, without reusing recurring structural patterns that could accelerate search. We introduce SymMatika, a hybrid SR algorithm that combines multi-island genetic programming (GP) with a reusable motif library inspired by biological sequence analysis. SymMatika identifies high-impact substructures in top-performing candidates and reintroduces them to guide future generations. Additionally, it incorporates a feedback-driven evolutionary engine and supports both explicit and implicit relation discovery using implicit-derivative metrics. Across benchmarks, SymMatika achieves state-of-the-art recovery rates on the Nguyen and Feynman benchmark suites, an impressive recovery rate of 61% on Nguyen-12 compared to the next best 2%, and strong placement on the error-complexity Pareto fronts on the Feynman equations and on a subset of 57 SRBench Black-box problems. Our results demonstrate the power of structure-aware evolutionary search for scientific discovery. To support broader research in interpretable modeling and symbolic discovery, we have open-sourced the full SymMatika framework.