# Deep Divide-and-Reduce in Symbolic Regression

arXiv: https://arxiv.org/abs/2608.02628 · HTML: https://mlsanity.com/paper/2608.02628/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [MetaSymNet: A Tree-like Symbol Network with Adaptive Architecture and Activation Functions](https://mlsanity.com/paper/2311.07326/) (2023)

## Abstract (arXiv)

Symbolic regression (SR) aims to discover underlying mathematical expressions from data while preserving interpretability. Most existing learning-based SR methods primarily optimize expressions from observations without explicitly exploiting their structural mathematical properties. AI Feynman introduced a complementary paradigm that leverages such properties to recursively decompose complex expressions, but its decomposition criteria cover only restricted structural forms and its treatment of nested composition can require brute-force search over candidate sub-expressions. Building on this paradigm, we propose Deep Divide-and-Reduce in Symbolic Regression (DDRSR), a mathematically grounded framework that systematically generalizes expression decomposition and variable reduction. DDRSR extends translational symmetry to coefficient- and exponent-interfered forms, enables variable separation under overlapping variables and additive constant offsets, and generalizes the identification of nested compositional structures. We further characterize an intrinsic non-identifiability limitation of decomposition when no effective variable separation is induced. Experiments across multiple symbolic regression algorithms and benchmark datasets show that DDRSR identifies a broader range of decomposable structures than AI Feynman and overall improves downstream regression accuracy and exact-expression recovery.