{"ID":2844542,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.05849","arxiv_id":"2511.05849","title":"EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph","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). 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.","short_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 direc...","url_abs":"https://arxiv.org/abs/2511.05849","url_pdf":"https://arxiv.org/pdf/2511.05849v2","authors":"[\"Nan Jiang\",\"Ziyi Wang\",\"Yexiang Xue\"]","published":"2025-11-08T04:39:11Z","proceeding":"cs.SC","tasks":"[\"cs.SC\",\"cs.AI\",\"cs.LG\"]","methods":"[\"Reinforcement Learning\",\"Large Language Model\",\"Language Model\",\"LoRA\"]","has_code":false}