# DN-CL: Deep Symbolic Regression against Noise via Contrastive Learning

arXiv: https://arxiv.org/abs/2406.14844 · HTML: https://mlsanity.com/paper/2406.14844/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 36 references that are in the map.
- First posted on arXiv 21 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [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)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Controllable Neural Symbolic Regression](https://mlsanity.com/paper/2304.10336/) (2023)
- [MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task](https://mlsanity.com/paper/2402.18603/) (2024)

## Built on by (most cited first, 1 of 1)

- [Beyond Least Squares: Robust Regression Transformer (R2T)](https://mlsanity.com/paper/2508.02874/) (2025)

## Abstract (arXiv)

Noise ubiquitously exists in signals due to numerous factors including physical, electronic, and environmental effects. Traditional methods of symbolic regression, such as genetic programming or deep learning models, aim to find the most fitting expressions for these signals. However, these methods often overlook the noise present in real-world data, leading to reduced fitting accuracy. To tackle this issue, we propose textitDeep Symbolic Regression against Noise via Contrastive Learning (DN-CL). DN-CL employs two parameter-sharing encoders to embed data points from various data transformations into feature shields against noise. This model treats noisy data and clean data as different views of the ground-truth mathematical expressions. Distances between these features are minimized, utilizing contrastive learning to distinguish between 'positive' noise-corrected pairs and 'negative' contrasting pairs. Our experiments indicate that DN-CL demonstrates superior performance in handling both noisy and clean data, presenting a promising method of symbolic regression.