Machine learning phase transitions: Connections to the Fisher information
This work provides theoretical insights into machine-learning methods for phase transitions, which is important for researchers in physics and machine learning, though it is incremental as it builds on existing information geometry tools.
The authors tackled the problem of understanding the working principles and limitations of machine-learning techniques for detecting phase transitions by connecting them to information-theoretic concepts, specifically proving that these indicators approximate the square root of the Fisher information and demonstrating this numerically for classical and quantum systems.
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.