John W. Clark

Ziyuan Li, Paulo S. A. Freitas, John W. Clark et al.

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.

Babette Dellen, Uwe Jaekel, Paulo S. A. Freitas et al.

Accurate estimation of nuclear masses and their prediction beyond the experimentally explored domains of the nuclear landscape are crucial to an understanding of the fundamental origin of nuclear properties and to many applications of nuclear science, most notably in quantifying the $r$-process of stellar nucleosynthesis. Neural networks have been applied with some success to the prediction of nuclear masses, but they are known to have shortcomings in application to extrapolation tasks. In this work, we propose and explore a novel type of neural network for mass prediction in which the usual neuron-like processing units are replaced by complex-valued product units that permit multiplicative couplings of inputs to be learned from the input data. This generalized network model is tested on both interpolation and extrapolation data sets drawn from the Atomic Mass Evaluation. Its performance is compared with that of several neural-network architectures, substantiating its suitability for nuclear mass prediction. Additionally, a prediction-uncertainty measure for such complex-valued networks is proposed that serves to identify regions of expected low prediction error.

Aditya Cowsik, John W. Clark

A two-layer neural network model that systematically includes correlations among input variables to arbitrary order and is designed to implement Bayes inference has been adapted to classify breast cancer tumors as malignant or benign, assigning a probability for either outcome. The inputs to the network represent measured characteristics of cell nuclei imaged in Fine Needle Aspiration biopsies. The present machine-learning approach to diagnosis (known as HOPP, for higher-order probabilistic perceptron) is tested on the much-studied, open-access Breast Cancer Wisconsin (Diagnosis) Data Set of Wolberg et al. This set lists, for each tumor, measured physical parameters of the cell nuclei of each sample. The HOPP model can identify the key factors -- input features and their combinations -- most relevant for reliable diagnosis. HOPP networks were trained on 90\% of the examples in the Wisconsin database, and tested on the remaining 10\%. Referred to ensembles of 300 networks, selected randomly for cross-validation, accuracy of classification for the test sets of up to 97\% was readily achieved, with standard deviation around 2\%, together with average Matthews correlation coefficients reaching 0.94 indicating excellent predictive performance. Demonstrably, the HOPP is capable of matching the predictive power attained by other advanced machine-learning algorithms applied to this much-studied database, over several decades. Analysis shows that in this special problem, which is almost linearly separable, the effects of irreducible correlations among the measured features of the Wisconsin database are of relatively minor importance, as the Naive Bayes approximation can itself yield predictive accuracy approaching 95\%. The advantages of the HOPP algorithm will be more clearly revealed in application to more challenging machine-learning problems.