# EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph

arXiv: https://arxiv.org/abs/2511.05849 · HTML: https://mlsanity.com/paper/2511.05849/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 79 references that are in the map.
- First posted on arXiv 8 Nov 2025.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [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)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Stochastic Variance-Reduced Policy Gradient](https://mlsanity.com/paper/1806.05618/) (2018)
- [On Learning Intrinsic Rewards for Policy Gradient Methods](https://mlsanity.com/paper/1804.06459/) (2018)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [The Value Equivalence Principle for Model-Based Reinforcement Learning](https://mlsanity.com/paper/2011.03506/) (2020)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [The Optimal Reward Baseline for Gradient-Based Reinforcement Learning](https://mlsanity.com/paper/1301.2315/) (2013)
- [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)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge](https://mlsanity.com/paper/2209.06257/) (2022)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Learning Continuous Semantic Representations of Symbolic Expressions](https://mlsanity.com/paper/1611.01423/) (2016)
- [Neural Program Synthesis with Priority Queue Training](https://mlsanity.com/paper/1801.03526/) (2018)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [Evolving symbolic density functionals](https://mlsanity.com/paper/2203.02540/) (2022)
- [Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert](https://mlsanity.com/paper/2308.09474/) (2023)
- [A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data](https://mlsanity.com/paper/2309.13705/) (2023)

## Built on by (most cited first, 2 of 2)

- [SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery](https://mlsanity.com/paper/2511.10833/) (2025)
- [SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery](https://mlsanity.com/paper/2609.04639/) (2026)

## Abstract (arXiv)

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression renders the task computationally challenging. A promising yet underexplored direction for reducing the search space and accelerating training lies in *symbolic equivalence*: many expressions, although syntactically different, define the same function -- for example, log(x12x23), log(x12)+log(x23), and 2log(x1)+3log(x2). Existing algorithms treat such variants as distinct outputs, leading to redundant exploration and slow learning. We introduce EGG-SR, a unified framework that integrates symbolic equivalence into a class of modern symbolic regression methods, including Monte Carlo Tree Search (MCTS), Deep Reinforcement Learning (DRL), and Large Language Models (LLMs). EGG-SR compactly represents equivalent expressions through the proposed EGG module (via equality graphs), accelerating learning by: (1) pruning redundant subtree exploration in EGG-MCTS, (2) aggregating rewards across equivalent generated sequences in EGG-DRL, and (3) enriching feedback prompts in EGG-LLM. Theoretically, we show the benefit of embedding EGG into learning: it tightens the regret bound of MCTS and reduces the variance of the DRL gradient estimator. Empirically, EGG-SR consistently enhances a class of symbolic regression models across several benchmarks, discovering more accurate expressions within the same time limit. Project page is at: https://nan-jiang-group.github.io/egg-sr.