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

Nan Jiang, Ziyi Wang, Yexiang Xue

Keywords: Symbolic Regression, symbolic equivalence, Monte Carlo Tree Search, Deep Reinforcement Learning, Large Language Model

TL;DR: We introduce EGG-SR, a unified framework that integrates equality graphs (e-graphs) into diverse symbolic regression algorithms.

Abstract:

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, $\log(x_1^2x_2^3)$, $\log(x_1^2)+\log(x_2^3)$, and $2\log(x_1)+3\log(x_2)$.
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).
\method-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.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 10593