UCLA

After an introduction which gives a brief overview of the relevant machine learning topics, we begin chapter 1 by introducing the phenomenon of many-body localization (MBL). We emphasize its significance by contrasting many-body localized states with thermal states, and describe efforts to distinguish the two phases. We then move on to describe the phenomenological picture of MBL which makes use of local integrals of motion (LIOMs). This enlightening picture explains many of the features of MBL, and has inspired various renormalization group approaches to understanding the phase. We illustrate the intuition for this picture using one such numerical RG scheme known as the Spectrum Bifurcation Renormalization Group, which allows one to construct iterative diagonalizing unitaries and obtain a LIOM representation of a given Hamiltonian.

After introducing the topic of many-body localization, we describe an application of unsupervised learning to the problem of distinguishing distinct phases within the MBL regime. This begins with a discussion of many-body localized phases, and the difficulty of identifying them. We then give an approach to this problem using a form of unsupervised learning, in which eigenstates are classified by clustering them according to their entanglement spectra. This is compared to the state of the art approach, which uses supervised learning. Despite the comparable results of the two methods, the unsupervised technique introduced relies on no labeled data. Potential applications as well as limitations of the method are then described.

In chapter 2, we recount recent research which applies a physics-based approach in order to understand the training dynamics of a class of machine learning models known as generative adversarial networks (GANs). This begins with an introduction to GANs, and a description of GAN training.Emphasizing the difficulty of training GANs, we then outline a very common problematic phenomenon within GAN training, known as mode collapse, in which outputs fail to become sufficiently diverse.

We then distill the key features necessary to observe this phenomenon of GAN failure,and construct a toy model for GAN training in which we can study it with more clarity. Finally, within this toy model, we are able to identify a phase transition, separating the regime of successful training from the regime of mode collapse. Additionally, we diagnose the source of this transition. We conclude by remarking on potential applications of such a result to a more realistic GAN setting.