Deep learning is a broad set of techniques that uses multiple layers of representation to automatically learn relevant features directly from structured data. Recently, such techniques have yielded record-breaking results on a diverse set of difficult machine learning tasks in computer vision, speech recognition, and natural language processing. Despite the enormous success of deep learning, relatively little is understood theoretically about why these techniques are so successful at feature learning and compression. Here, we show that deep learning is intimately related to one of the most important and successful techniques in theoretical physics, the renormalization group (RG). RG is an iterative coarse-graining scheme that allows for the extraction of relevant features (i.e. operators) as a physical system is examined at different length scales. We construct an exact mapping from the variational renormalization group, first introduced by Kadanoff, and deep learning architectures based on Restricted Boltzmann Machines (RBMs). We illustrate these ideas using the nearest-neighbor Ising Model in one and two-dimensions. Our results suggests that deep learning algorithms may be employing a generalized RG-like scheme to learn relevant features from data.

本文研究深度学习的理论基础，发现其与理论物理中的重整化群技术密切相关，提供了一种新的理解思路，解释了深度学习技术在数据特征学习和压缩方面的成功，同时探究抽取相关特征的机制和算法。

变分重整化群与深度学习之间的精确映射