Beyond Prediction: Structural Transfer and Partial Identification in Symbolic Domain Generalization

Computational models of human learning and memory aim to discover concise and interpretable relationships among practice history, temporal intervals, and subsequent recall outcomes. Symbolic regression provides a direct approach toward this goal; however, in heterogeneous learning environments, good fit on a single dataset or recurring expressions across multiple environments do not necessarily indicate transferable structures, nor do they reveal which structural components truly receive cross-environment evidential support. To address this issue, we propose Cross-Fitted Domain-Robust Symbolic Regression (CF-DRSR), an evidence-calibrated framework for cross-environment symbolic modeling. CF-DRSR separates symbolic discovery, transfer validation, and structural identification: it constructs comparable candidate structural families through symbolic search and structural alignment, evaluates the transfer support of candidate structures on data not involved in discovery through source-held-out predictive qualification, and characterizes identifiable structural content under multiple compatible explanations through set-valued structural identification. Experiments on multiple heterogeneous learning datasets demonstrate that CF-DRSR achieves effective prediction on unseen domains while revealing the environment-dependent transfer scope and boundaries of candidate structures. Further analysis shows that recurring predictive structures do not necessarily correspond to uniquely identifiable laws, as multiple structural explanations may remain consistent with the available evidence. These findings suggest that cross-environment symbolic modeling should distinguish among three levels: predictive generalization, structural transfer, and structural identification.