RQC Seminar
24th RQC Seminar
講演者
Dr. Vittorio Vitale
(CMSP Group, ICTP, Italy)日程
2023年1月20日(金)16:00-17:00(JST)
開催場所
ハイブリッド(Zoom ・ 理研 和光事業所 本部棟2階 大会議室)
講演タイトル
Unsupervised learning via the Intrinsic Dimension
お問合せ
rqc_info[at]ml.riken.jp
講演概要
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.