Artificial Neural Network Field Theory in Nuclear Physics

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics.

However, these ANNs are typically treated as ``black boxes'', where their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters are empirically chosen by optimizing learning with limited exploration.

We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width.

This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory.