Machine learning phase transitions: Connections to the Fisher information

Author:

Julian Arnold, Niels Lörch, Flemming Holtorf, Frank Schäfer

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Machine Learning (cs.LG), Quantum Physics (quant-ph), Machine Learning (stat.ML)

journal:

date:

2023-11-17 00:00:00

Abstract

Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential failure modes of these techniques by rooting popular machine-learning indicators of phase transitions in information-theoretic concepts. Using tools from information geometry, we prove that several machine-learning indicators of phase transitions approximate the square root of the system's (quantum) Fisher information from below -- a quantity that is known to indicate phase transitions but is often difficult to compute from data. We numerically demonstrate the quality of these bounds for phase transitions in classical and quantum systems.

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