# A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data

arXiv: https://arxiv.org/abs/2309.13705 · HTML: https://mlsanity.com/paper/2309.13705/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [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)
- [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)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [RSRM: Reinforcement Symbolic Regression Machine](https://mlsanity.com/paper/2305.14656/) (2023)
- [Interaction-Transformation Evolutionary Algorithm for Symbolic Regression](https://mlsanity.com/paper/1902.03983/) (2019)

## Built on by (most cited first, 16 of 16)

- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization](https://mlsanity.com/paper/2310.05537/) (2023)
- [Improving Monte Carlo Tree Search for Symbolic Regression](https://mlsanity.com/paper/2509.15929/) (2025)
- [Smart Vision-Language Reasoners](https://mlsanity.com/paper/2407.04212/) (2024)
- [Complexity-Aware Deep Symbolic Regression with Robust Risk-Seeking Policy Gradients](https://mlsanity.com/paper/2406.06751/) (2024)
- [Ab Initio Nonparametric Variable Selection for Scalable Symbolic Regression with Large p](https://mlsanity.com/paper/2410.13681/) (2024)
- [Closed-form Solutions: A New Perspective on Solving Differential Equations](https://mlsanity.com/paper/2405.14620/) (2024)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [Enhancing Symbolic Regression and Universal Physics-Informed Neural Networks with Dimensional Analysis](https://mlsanity.com/paper/2411.15919/) (2024)
- [SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving](https://mlsanity.com/paper/2602.03816/) (2026)
- [Architecture-Induced Recoverability Bias in Differentiable Symbolic Regression](https://mlsanity.com/paper/2604.23256/) (2026)
- [UniSymNet: A Unified Symbolic Network Guided by Transformer](https://mlsanity.com/paper/2505.06091/) (2025)
- [Beyond Error-Based Optimization: Experience-Driven Symbolic Regression with Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2601.14693/) (2026)
- [GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing](https://mlsanity.com/paper/2605.10685/) (2026)
- [MOSAIC-SR: Transformer-Guided Symbolic Regression for Scientific Equation Recovery](https://mlsanity.com/paper/2609.20997/) (2026)
- [MorphingNet: Symbolic Regression Where the Network Is the Formula](https://mlsanity.com/paper/2610.19942/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However, these methods face difficulties in processing high-dimensional problems and learning constants due to the large search space, and they don't scale well to unseen problems. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore symbolic networks with various structures, guided by reinforcement learning, and optimize them to identify expressions that better-fitting the data. Based on extensive numerical experiments on low-dimensional public standard benchmarks and the well-known SRBench with more variables, DySymNet shows clear superiority over several representative baseline models. Open source code is available at https://github.com/AILWQ/DySymNet.