# Online Symbolic Regression with Informative Query

arXiv: https://arxiv.org/abs/2302.10539 · HTML: https://mlsanity.com/paper/2302.10539/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 21 Feb 2023.

## Builds on (most cited first, 25 of 25)

- [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)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [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)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [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)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [Multi-label Contrastive Predictive Coding](https://mlsanity.com/paper/2007.09852/) (2020)
- [Fast, accurate, and transferable many-body interatomic potentials by symbolic regression](https://mlsanity.com/paper/1904.01095/) (2019)
- [Symbolic Learning to Optimize: Towards Interpretability and Scalability](https://mlsanity.com/paper/2203.06578/) (2022)
- [Elite Bases Regression: A Real-time Algorithm for Symbolic Regression](https://mlsanity.com/paper/1704.07313/) (2017)
- [Active Learning Improves Performance on Symbolic RegressionTasks in StackGP](https://mlsanity.com/paper/2202.04708/) (2022)
- [Integrating Auxiliary Information in Self-supervised Learning](https://mlsanity.com/paper/2106.02869/) (2021)
- [Learning to Acquire Information](https://mlsanity.com/paper/1704.06131/) (2017)
- [Information-Geometric Set Embeddings (IGSE): From Sets to Probability Distributions](https://mlsanity.com/paper/1911.12463/) (2019)
- [Neural Program Synthesis with Query](https://mlsanity.com/paper/2205.07857/) (2022)

## Built on by (most cited first, 2 of 2)

- [Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching](https://mlsanity.com/paper/2409.01416/) (2024)
- [From Passive Reuse to Active Reasoning: Grounding Large Language Models for Neuro-Symbolic Experience Replay](https://mlsanity.com/paper/2605.09419/) (2026)

## Abstract (arXiv)

Symbolic regression, the task of extracting mathematical expressions from the observed data  vxi, yi , plays a crucial role in scientific discovery. Despite the promising performance of existing methods, most of them conduct symbolic regression in an textitoffline setting. That is, they treat the observed data points as given ones that are simply sampled from uniform distributions without exploring the expressive potential of data. However, for real-world scientific problems, the data used for symbolic regression are usually actively obtained by doing experiments, which is an textitonline setting. Thus, how to obtain informative data that can facilitate the symbolic regression process is an important problem that remains challenging. In this paper, we propose QUOSR, a query-based framework for online symbolic regression that can automatically obtain informative data in an iterative manner. Specifically, at each step, QUOSR receives historical data points, generates new vx, and then queries the symbolic expression to get the corresponding y, where the (vx, y) serves as new data points. This process repeats until the maximum number of query steps is reached. To make the generated data points informative, we implement the framework with a neural network and train it by maximizing the mutual information between generated data points and the target expression. Through comprehensive experiments, we show that QUOSR can facilitate modern symbolic regression methods by generating informative data.