Symbolic regression aims to recover closed-form expressions from numerical data, but in differentiable symbolic regression the recovered expression depends not only on the grammar but also on the fixed architecture through which variables are routed during training. This is relevant to signal-processing settings in which closed-form models and interpretable nonlinear structure are useful. This architecture-specific effect has rarely been isolated directly, because existing comparisons often vary architecture together with operator family, grammar, or search procedure. Three depth-3 architectures are compared across twenty-four operator--shape--leaf combinations, holding operator family, grammar, and training protocol fixed as far as possible while varying the variable-routing architecture. Recovery changes from $0/64$ to $64/64$ trials on the same target under an architecture-plus-native-training-protocol comparison. The best architecture on one target is the worst on another, and trees with two equal-depth subtrees fail in every configuration tested ($0/3{,}776$). As a proof-of-concept mitigation, a small architecture set is trained and the hardened expression with the lowest held-out RMSE is selected. On the jointly-run subset, this improves recovery from $34.4\%$ for the only architecture present in all three configurations to $50.1\%$. On a Shockley diode target, the validation selector recovers cases missed by that baseline architecture, which by itself recovers $0/32$ seeds. Since the jointly-run subset contains only three configurations, the selector result is evidence that validation-based architecture selection is promising, not a complete benchmark. These results support treating architecture as a measurable design variable that should be reported, stress-tested, and selected using held-out validation rather than fixed a priori.

翻译：符号回归旨在从数值数据中恢复闭式表达式，但在可微符号回归中，恢复的表达式不仅取决于语法，还取决于训练过程中变量传递的固定架构。这对闭式模型和可解释非线性结构有用的信号处理场景具有重要意义。现有比较通常同时改变架构与算子族、语法或搜索过程，因此这种特定于架构的效应很少被直接分离。本文在保持算子族、语法和训练协议尽可能固定的前提下，通过比较三种深度为3的架构，在24种算子-形状-叶子组合上通过改变变量传递架构进行实验。在架构与本机训练协议的比较中，同一目标的恢复结果从0/64次试验变为64/64次试验。某一目标的最优架构在另一目标上变为最差，而具有两个等深子树的树在所有测试配置中均失败（0/3,776次）。作为概念验证缓解方案，训练一个小型架构集，并选择具有最低保留均方根误差的强化表达式。在联合运行子集中，该方案将恢复率从唯一出现在所有三种配置中的架构的34.4%提升至50.1%。针对肖克利二极管目标，验证选择器恢复了基线架构遗漏的案例，而该基线架构本身仅恢复0/32次种子。由于联合运行子集仅包含三种配置，选择器结果仅表明基于验证的架构选择具有前景，而非完整基准。这些结果支持将架构视为可测量的设计变量，应通过保留验证而非先验固定来报告、压力测试和选择。