Finite-Size Effects in Machine Learning the Kosterlitz-Thouless Transition

Recently, machine learning (ML) algorithms have found use in physics as promising novel tools that might overcome the limitations faced by the standard computational methods. First applications proved successful in classifying conventional phases of matter which can be detected based on a local order parameter. The natural next step is the examination of topological phases and phase transitions. In this talk I present the study of the Kosterlitz-Thouless transition in the classical 2D XY model with supervised ML methods. I will show the results obtained from training a simple feed-forward and a convolutional network on Monte-Carlo sampled spin configurations. In particular, I will discuss why the networks fail to learn topological features from raw input data and how the semi-supervised confusion scheme provides indications for that the networks’ classification relies on local magnetization which is a finite-size artifact.