EditFlowSR: Revisable Expression Generation for Symbolic Regression

Symbolic regression (SR) aims to discover compact, interpretable mathematical expressions from data. This goal inherently requires iterative refinement rather than one-shot construction. Autoregressive methods lack the ability to perform targeted corrections, so whenever structural flaws appear, the remainder of the sequence must be discarded and regenerated. Meanwhile, search-based methods rely on costly and indirect replacement through enumeration. We propose EditFlowSR, which reframes SR as iterative editing of expression trees through insertions, deletions, and substitutions. To reconcile fitting accuracy with algebraic simplicity, we introduce dual trajectory supervision. One trajectory teaches the model to construct expressions from data, while the other teaches it to algebraically simplify them, and both are unified under the shared editing framework. At inference time, EditFlowSR starts from a randomly initialized expression and progressively refines it through iterative editing, simultaneously constructing valid structure and removing redundancy. Across the standard SRBench, EditFlowSR achieves first-rank Pareto dominance in predictive accuracy, expression tree size, and time complexity. These results establish edit-based generation as a principled and effective paradigm for end-to-end symbolic regression. Code is available at \url{https://anonymous.4open.science/r/EditFlowSR_NIPS2026}.