Criticality Analysis of Artifical Neural Networks in Nuclear Physics*

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs), have become extremely useful tools in nuclear physics.

However ANNs often are treated as "black boxes", where their architecture (width, depth, and weight/bias initialization) is decided empirically based on what allows them to be trained most effectively. To actually investigate the principles of neural network architecture in a non-empirical, method based way, some have turned to performing criticality arguments with renormalization group flows in terms of the hyperparameters for weight/bias initialization and the ratio of depth to width. These criticality arguments are meant to tune these hyperparameters to give an effective theory of the neural network as an expansion in the ratio of depth to width. This allows for the study of properties of neural networks so they can have a more ideal architecture chosen from the beginning, giving a methodology to improve many projects in nuclear physics utilizing ANNs.  I’ll present preliminary studies using criticality analyses geared towards nuclear physics.