# Statistical learnability of nuclear masses

## TL;DR

This paper applies statistical learning theory to nuclear mass prediction, establishing bounds on prediction errors, validating them with neural networks, and comparing with existing models to understand the limits of nuclear structure modeling.

## Contribution

It introduces a statistical learning framework to bound nuclear mass prediction errors and validates these bounds with neural network experiments, highlighting the limits of current nuclear models.

## Key findings

- Neural network predictions align with statistical bounds.
- Mass model errors are near the theoretical limits.
- Nuclear models operate at the edge of learnability.

## Abstract

After more than 80 years from the seminal work of Weizs\"acker and the liquid drop model of the atomic nucleus, deviations from experiments of mass models ($\sim$ MeV) are orders of magnitude larger than experimental errors ($\lesssim$ keV). Predicting the mass of atomic nuclei with precision is extremely challenging. This is due to the non--trivial many--body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. Statistical theory of learning will be used to provide bounds to the prediction errors of model trained with a finite data set. These bounds are validated with neural network calculations, and compared with state of the art mass models. Therefore, it will be argued that the nuclear structure models investigating ground state properties explore a system on the limit of the knowledgeable, as defined by the statistical theory of learning.