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.

翻译：尽管基于机器学习从数据中检测相变的技术已广泛使用且取得显著成功，但其工作原理与基本局限仍难以捉摸。本文通过将流行的机器学习相变指标植根于信息论概念，揭示了这些技术的内部机制并识别了潜在失效模式。借助信息几何工具，我们证明多种机器学习相变指标从下方逼近系统（量子）Fisher信息的平方根——该量虽已知可指示相变，但通常难以从数据中计算。我们通过经典与量子系统的相变实例，数值验证了这些下界的有效性。