24th RQC Seminar
Dr. Vittorio Vitale
(CMSP Group, ICTP, Italy）
ハイブリッド（Zoom ・ 理研 和光事業所 本部棟2階 大会議室）
Unsupervised learning via the Intrinsic Dimension
The identification of universal properties from minimally processed data sets is one goal of machine learning techniques. Both in supervised or unsupervised settings, “making sense” of hitherto unseen raw data is defined at the outset, by encoding the task (regression, classification, etc.) in an objective function. This turns learning and inference into an optimisation problem. Here, starting from data-sets sampled from classical partition functions and one-dimensional quantum models, we build networks (graphs) by drawing links between the points according to a cutoff distance that is determined by the data structure and the choice of metric. Remarkably, this enables a transfer of methods and concepts from disconnected fields that allow us to tackle in an agnostic way the study of phase transition in several models. We observe how the minimum number of variables needed to accurately describe the important features of a data-set, the intrinsic dimension Id, behaves in the vicinity of phase transitions. We show how the finite-size analysis of the Id allows us to identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters. We review previous works [Physical Review X 11 (1), 011040] and elaborate on the topic with new results in case of classical systems with topological defects and ground states of one-dimensional quantum systems.