# Prompting Neural-Guided Equation Discovery Based on Residuals

arXiv: https://arxiv.org/abs/2511.05586 · HTML: https://mlsanity.com/paper/2511.05586/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Plan-and-Solve Prompting: Improving Zero-Shot Chain-of-Thought Reasoning by Large Language Models](https://mlsanity.com/paper/2305.04091/) (2023)
- [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)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Learning Loss for Test-Time Augmentation](https://mlsanity.com/paper/2010.11422/) (2020)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [Symbolic Regression via Control Variable Genetic Programming](https://mlsanity.com/paper/2306.08057/) (2023)
- [Racing Control Variable Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2309.07934/) (2023)

## Abstract (arXiv)

Neural-guided equation discovery systems use a data set as prompt and predict an equation that describes the data set without extensive search. However, if the equation does not meet the user's expectations, there are few options for getting other equation suggestions without intensive work with the system. To fill this gap, we propose Residuals for Equation Discovery (RED), a post-processing method that improves a given equation in a targeted manner, based on its residuals. By parsing the initial equation to a syntax tree, we can use node-based calculation rules to compute the residual for each subequation of the initial equation. It is then possible to use this residual as new target variable in the original data set and generate a new prompt. If, with the new prompt, the equation discovery system suggests a subequation better than the old subequation on a validation set, we replace the latter by the former. RED is usable with any equation discovery system, is fast to calculate, and is easy to extend for new mathematical operations. In experiments on 53 equations from the Feynman benchmark, we show that it not only helps to improve all tested neural-guided systems, but also all tested classical genetic programming systems.