EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification

2026-06-05

AI Summary

Neural symbolic regression often suffers from error accumulation during autoregressive decoding, leading to syntactically invalid mathematical expressions—particularly in complex scenarios where performance degrades significantly. To address this issue, this work proposes EditSR, a two-stage framework that first generates an initial expression using a neural symbolic model and then refines it via a pretrained, edit-based corrector through local posterior optimization. The corrector models the repair process as a grammar-constrained state-transition chain, ensuring that each editing step operates strictly within the space of valid expressions and allowing later edits to rectify earlier mistakes, thereby mitigating error propagation. Experimental results demonstrate that EditSR substantially improves the accuracy of symbolic structure recovery with negligible additional computational overhead, especially excelling on complex expressions.

Abstract

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.

Problem

• neural symbolic regression
• error accumulation
• autoregressive decoding
• expression rectification
• structural correctness

Innovation

• neural symbolic regression
• edit-based rectification
• error accumulation mitigation
• syntactically valid editing
• state-transition rectifier