arXiv2026
Ab initio theory establishes Wigner's SU(4) and Elliott's SU(3) as dominant symmetries of the nuclear force in light and intermediate-mass nuclei. Previous work shows the relevance of the former symmetry for nuclear binding, whether the latter organizes binding remains elusive. We probe whether both these symmetries organize nuclear masses, aiming at physical insights through interpretable models and predictive capability. From the SU(3) and SU(4) Casimirs we build 3 neural-network models. Two are conventional, a feature-informed NN (FINN) and a Gaussian variant (GINN) with predictive spread, while Wigner-informed network (WINN) is a new design constraining the mass formula to be linear in the operators, learning their (N,Z)-dependent couplings, so that the model is intrinsically explainable. All are trained on AME2016 subtracted by the liquid drop model at 4 data fractions and validated on nuclei new to AME2020, with extrapolation benchmarked against HFB-26 and r-process. The Casimir features carry binding information far beyond the bulk, and SHAP analysis suggests the quadratic SU(4) Casimir as the leading contributor to the residual binding. The WINN yields the best performance, reaching a 0.412 MeV validation error and competitive with state-of-the-art models, and importantly, when trained on the sparsest dataset it outperforms the other NNs trained on the densest. Off the known chart its masses track HFB-26 as closely as WS3 and reproduce the solar abundance peaks of a neutron-star-merger simulation. The WINN's coupling fields reveal an enhanced even-SU(4) contribution toward the neutron dripline, hinting at restoration of Wigner's symmetry. The SU(4) and SU(3) structures reach beyond individual nuclei to organize binding, and embedding symmetry-preserving operators directly in a domain-informed interpretable architecture yields a physically transparent model less hungry for data.