Rethinking Total Absorption Gamma Spectroscopy Deconvolution: Supervised Machine Learning vs Response-Matrix Methods

The extraction of $β$-feeding distributions in Total Absorption $γ$-ray Spectroscopy constitutes a challenging inverse problem, particularly in nuclei with complex decay schemes involving a large number of excited states. In such cases, the measured spectrum arises from the superposition of many detector response functions, making the determination of the individual feedings intrinsically ill-posed and highly sensitive to the methodology employed. In this work, we present a systematic comparison between supervised Machine-Learning techniques and Response-Matrix methods using realistic Monte Carlo simulations of an experimental Total Absorption Spectrometer. Supervised Machine-Learning approaches construct a non-parametric estimator that infers level feedings from the measured spectrum after a training stage, whereas Response-Matrix methods determine the feeding distribution by directly minimizing the difference between measured and reconstructed spectra. Our results show that supervised Machine-Learning techniques achieve superior accuracy in the reconstruction of individual feeding intensities, whereas Response-Matrix methods provide robust and physically consistent initial solutions. These findings support a hybrid strategy in which a Response-Matrix method is first used to obtain an initial feeding estimate, which is then refined using a supervised Machine-Learning approach to achieve improved overall accuracy.

Bridging Ab Initio Symmetries and Global Nuclear Masses with Interpretable Neural Networks

Ab initio modeling has established Wigner's SU(4) and Elliott's SU(3) as dominant symmetries of the nuclear force in light and intermediate-mass nuclei. We ask whether they also govern nuclear binding across the entire chart. Our aim is not high-precision prediction but physical insight, through interpretable, symmetry-based models. From the SU(3) and SU(4) Casimir operators we construct three neural-network (NN) mass models: Feature-Informed NN (FINN) for point predictions, Gaussian-Informed NN (GINN) adding uncertainty quantification, and Wigner-Informed NN (WINN) -- a mass formula using the Casimirs as an operator basis. All are trained on AME2016 and validated on nuclei new to AME2020. The SU(4) operators alone cut the root-mean-square error (RMSE) by nearly half on train and test data, and by about a fifth on extrapolation, relative to the liquid-drop baseline -- showing that Wigner's symmetry carries predictive information beyond bulk properties. Despite its compact form, WINN reaches the lowest validation RMSE, 0.430 MeV -- competitive with state-of-the-art mass models -- which we read less as a benchmark than as evidence that its symmetry basis captures important physics. WINN further reveals i) an enhancement of the quadratic SU(4) Casimir near the neutron dripline, signaling restoration of Wigner's symmetry, and ii) an unexpected gain of the quartic operator in the superheavy region. We thereby elevate emergent symmetries from the hidden order within individual nuclei to a governing principle of the whole nuclear chart.

Product units in gated recurrent units improve nuclear-mass prediction

The prediction of masses of atomic nuclei using machine learning can complement theoretical models and advance the exploration of poorly known domains of the nuclear chart. We propose a machine learning technique based on gated recurrent units (GRU), which have demonstrated competitive performance in nuclear-mass prediction by exploiting long-term dependencies. By integrating multiplicative interactions and product-unit transformations within recurrent units, we report significant improvements in nuclear-mass prediction. Computations are performed in the complex domain to jointly capture amplitude and phase dynamics. For interpolation and temporal-extrapolation tasks based on the atomic mass evaluation (AME2016 and AME2020), the complex additive-multiplicative product-unit gated recurrent unit (AM-PU-GRU) model consistently achieves the lowest prediction errors, with an interpolation RMSE of 0.227 $\pm$ 0.004 MeV and an extrapolation RMSE of 0.179 $\pm$ 0.015 MeV. These results surpass other state-of-the-art machine learning models and also outperform the real-valued GRU baseline and product-unit ablation variants, while remaining robust to different theoretical priors, including WS4 and SEMF. Our findings establish complex-valued product-unit recurrent networks as a new benchmark for sequence-based nuclear-mass prediction.