Parameter diagnostics of phases and phase transition learning by neural networks

TL;DR

This paper analyzes how shallow neural networks classify phases and phase transitions in condensed matter models, using weight matrices and filters to understand the physical quantities involved, and demonstrates diagnostic schemes for learning parameters.

Contribution

It introduces a method to diagnose neural network learning parameters and interpret physical quantities from shallow networks applied to phase classification tasks.

Findings

Neural network weights reveal physical order parameters.

Learning-by-confusing scheme effectively diagnoses learning parameters.

Convolutional networks perform well on vortex configurations in XY models.

Abstract

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were previously found to be efficient in classifying phases and locating phase transitions of various basic model systems. In order to rationalize the emergence of the classification process and for identifying any underlying physical quantities, it is feasible to examine the weight matrices and the convolutional filter kernels that result from the learning process of such shallow networks. Furthermore, we demonstrate how the learning-by-confusing scheme can be used, in combination with a simple threshold-value classification method, to diagnose the learning parameters of neural networks. In particular, we study the classification process of both fully-connected and convolutional neural networks for the two-dimensional Ising model with extended domain wall configurations included in the low-temperature regime. Moreover, we consider the two-dimensional XY model and contrast the performance of the learning-by-confusing scheme and convolutional neural networks trained on bare spin configurations to the case of preprocessed samples with respect to vortex configurations. We discuss these findings in relation to similar recent investigations and possible further applications.