Architecture-Induced Recoverability Bias in Differentiable Symbolic Regression

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.