# EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification

arXiv: https://arxiv.org/abs/2606.07915 · HTML: https://mlsanity.com/paper/2606.07915/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 71 references that are in the map.
- First posted on arXiv 6 Jun 2026.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (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)
- [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)
- [Levenshtein Transformer](https://mlsanity.com/paper/1905.11006/) (2019)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [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 with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [DiffusER: Discrete Diffusion via Edit-based Reconstruction](https://mlsanity.com/paper/2210.16886/) (2022)
- [Learning to Model Editing Processes](https://mlsanity.com/paper/2205.12374/) (2022)
- [EDITOR: an Edit-Based Transformer with Repositioning for Neural Machine Translation with Soft Lexical Constraints](https://mlsanity.com/paper/2011.06868/) (2020)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)

## Abstract (arXiv)

Neural symbolic regression models improve inference efficiency by shifting structural search to pretraining, but their one-pass autoregressive decoding is prone to error accumulation, which may lead to generating structurally incorrect expressions, especially in complex expression generation scenarios. Existing rectification strategies can alleviate this issue, but they often depend on restarting global search, thereby weakening the efficiency advantage of neural models, and remain susceptible to error accumulation. In this paper, we propose EditSR, a two-layer framework that combines a neural symbolic regression model in the first layer with an edit-based Rectifier in the second layer to achieve efficient prediction and post-hoc rectification. Instead of restarting the global search, we maintain rectification efficiency by pretraining the Rectifier. Specifically, we formulate the rectification process as a step-by-step state-transition chain starting from an incorrect expression, and develop a state-transition algorithm to construct supervised rectification chains for training the Rectifier. To ensure syntactic validity throughout rectification, each edit action is restricted to a syntactically valid space so that every edited expression remains parseable. In addition, because each edit decision is conditioned on the current state rather than the history, the Rectifier allows errors made in earlier steps to be rectified by subsequent edits, thereby reducing the risk of error accumulation. Extensive experiments and ablation studies show that EditSR substantially improves symbolic structure recovery with limited extra cost, with more pronounced gains on complex expressions, where one-pass autoregressive decoding is more susceptible to error accumulation.