# Product units in gated recurrent units improve nuclear-mass prediction

arXiv: https://arxiv.org/abs/2606.06866 · HTML: https://mlsanity.com/paper/2606.06866/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 26 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Predicting nuclear masses with product-unit networks](https://mlsanity.com/paper/2305.04675/) (2023)
- [PURe: A Plug-and-Play Product-Unit Residual Module for Vision Networks](https://mlsanity.com/paper/2505.04397/) (2025)
- [Discovering Nuclear Models from Symbolic Machine Learning](https://mlsanity.com/paper/2404.11477/) (2024)

## Abstract (arXiv)

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 ± 0.004 MeV and an extrapolation RMSE of 0.179 ± 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.