# ParFam -- (Neural Guided) Symbolic Regression Based on Continuous Global Optimization

arXiv: https://arxiv.org/abs/2310.05537 · HTML: https://mlsanity.com/paper/2310.05537/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Builds on (most cited first, 16 of 16)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (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)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [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, 10 of 10)

- [A Neural Symbolic Model for Space Physics](https://mlsanity.com/paper/2503.07994/) (2025)
- [When is a System Discoverable from Data? Discovery Requires Chaos](https://mlsanity.com/paper/2511.08860/) (2025)
- [ViSymRe: Vision Multimodal Symbolic Regression](https://mlsanity.com/paper/2412.11139/) (2024)
- [UniSymNet: A Unified Symbolic Network Guided by Transformer](https://mlsanity.com/paper/2505.06091/) (2025)
- [Interpretable Robotic Friction Learning via Symbolic Regression](https://mlsanity.com/paper/2505.13186/) (2025)
- [Symbolic recovery of PDEs from measurement data](https://mlsanity.com/paper/2602.15603/) (2026)
- [EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification](https://mlsanity.com/paper/2606.07915/) (2026)
- [SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery](https://mlsanity.com/paper/2609.04639/) (2026)
- [Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench](https://mlsanity.com/paper/2610.18938/) (2026)
- [MorphingNet: Symbolic Regression Where the Network Is the Formula](https://mlsanity.com/paper/2610.19942/) (2026)

## Abstract (arXiv)

The problem of symbolic regression (SR) arises in many different applications, such as identifying physical laws or deriving mathematical equations describing the behavior of financial markets from given data. Various methods exist to address the problem of SR, often based on genetic programming. However, these methods are usually complicated and involve various hyperparameters. In this paper, we present our new approach ParFam that utilizes parametric families of suitable symbolic functions to translate the discrete symbolic regression problem into a continuous one, resulting in a more straightforward setup compared to current state-of-the-art methods. In combination with a global optimizer, this approach results in a highly effective method to tackle the problem of SR. We theoretically analyze the expressivity of ParFam and demonstrate its performance with extensive numerical experiments based on the common SR benchmark suit SRBench, showing that we achieve state-of-the-art results. Moreover, we present an extension incorporating a pre-trained transformer network DL-ParFam to guide ParFam, accelerating the optimization process by up to two magnitudes. Our code and results can be found at https://github.com/Philipp238/parfam.