用编辑修正提升神经符号回归的结构准确性,避免重算却能有效纠错。
EditSR: Enhancing Neural Symbolic Regression via Edit-based Rectification

- 先用神经模型生成表达式,再通过可解析的编辑步骤逐步修正错误。
- 在复杂表达式上纠错成功率显著提升,额外开销很小。
- 适合需要高精度符号表达式生成的研究者,尤其擅长处理复杂结构。
神经符号回归模型通过预训练将结构搜索转移到预训练阶段,提升了推理效率,但其单次自回归解码易产生误差累积,导致结构错误,尤其在复杂表达式生成中更为明显。现有修正策略虽能缓解此问题,但常需重启全局搜索,削弱了神经模型的效率优势,且仍可能受误差累积影响。本文提出EditSR,一种两层框架:第一层为神经符号回归模型,第二层为基于编辑的修正器。修正器不重启全局搜索,而是通过预训练实现高效修正。我们将其修正过程建模为从错误表达式出发的逐步状态转移链,并设计状态转移算法构建监督修正链以训练修正器。每个编辑操作限定在语法有效的空间内,确保每一步修改后的表达式始终可解析。此外,每次编辑决策仅依赖当前状态而非历史,使早期错误可通过后续编辑纠正,降低误差累积风险。大量实验与消融研究显示,EditSR在几乎无额外成本下显著提升符号结构恢复能力,对复杂表达式的改进尤为明显。
原文摘要 · Abstract (English)
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.
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