Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from a theoretical point of view. The mathematical description of learning problems involves very large collections of interacting random variables, difficult to handle analytically as well as numerically. This complexity is precisely the object of study of statistical physics. Its mission, originally pointed toward natural systems, is to understand how macroscopic behaviors arise from microscopic laws. Mean-field methods are one type of approximation strategy developed in this view. We review a selection of classical mean-field methods and recent progress relevant for inference in neural networks. In particular, we remind the principles of derivations of high-temperature expansions, the replica method and message passing algorithms, highlighting t...

中文翻译：

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神经网络的均值推断方法

依靠深度​​神经网络的机器学习算法最近在人工智能方面实现了巨大飞跃。尽管它们的应用很流行，但是从理论的角度来看，这些算法的效率在很大程度上仍然无法解释。学习问题的数学描述涉及大量相互作用的随机变量集合，难以同时进行解析和数值处理。这种复杂性恰恰是统计物理学研究的对象。它的任务最初指向自然系统，目的是了解微观行为是如何从微观定律中产生的。在这种观点下，均值场方法是一种近似策略。我们回顾了经典平均场方法的选择以及与神经网络推理相关的最新进展。尤其是，