Statistical Physics through the Lens of Real-Space Mutual Information,Physical Review Letters

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Statistical Physics through the Lens of Real-Space Mutual Information
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-12-06 , DOI: 10.1103/physrevlett.127.240603
Doruk Efe Gökmen ₁ , Zohar Ringel ₂ , Sebastian D Huber ₁ , Maciej Koch-Janusz _{1,

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Affiliation

Identifying the relevant degrees of freedom in a complex physical system is a key stage in developing effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, lack formal interpretability. Here we present an algorithm employing state-of-the-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges, and use this advance to develop a new paradigm in identifying the most relevant operators describing properties of the system. We demonstrate this on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic constituents. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way toward automated theory building.

中文翻译：

从实空间互信息的角度看统计物理学

确定复杂物理系统中的相关自由度是开发平衡内外有效理论的关键阶段。著名的重整化组为此提供了一个框架，但它在不熟悉的系统中的实际执行充满了临时性选择，而机器学习方法虽然很有前途，但缺乏正式的可解释性。在这里，我们提出了一种算法，该算法在基于机器学习的信息理论量估计中采用最先进的结果，克服了这些挑战，并利用这一进步开发了一种新范式，用于识别描述系统。我们在交互模型上证明了这一点，其中出现的自由度与微观成分在性质上不同。我们的结果推动了机器学习正式可解释应用的边界，从概念上为自动化理论构建铺平了道路。

更新日期：2021-12-06

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