一种机器学习与相变之间的新型映射  

A novel mapping between machine learning and phase transition

作　　者：龙飞 黄琨 李峰[3] LONG Fei;HUANG Kun;LI Feng(Chinaso Inc, Beijing 100077, China;State Key Laboratory of Media Convergence Production Technology and Systems, Xinhua News Agency, Beijing 100803, China;Dept. of Automation, University of Science and Technology of China, Hefei 230027, China)

机构地区：[1]中国搜索信息科技股份有限公司,北京100077 [2]新华社媒体融合生产技术与系统国家重点实验室,北京100803 [3]中国科学技术大学自动化系,安徽合肥230027

出　　处：《中国科学技术大学学报》2020年第1期18-28,共11页JUSTC

摘　　要：相变是一个重要的物理概念,它代表着从一个热力学状态到另一个热力学状态的转变.它在凝聚态物理、粒子物理、天体物理等物理领域有着广泛的应用.机器学习是研究通过经验自动改进的计算机算法.近年来,随着深入学习的成功,它也是一个非常活跃的研究领域.于是从视觉上证明了监督学习的训练过程与阶段过渡过程十分相似,有可能确定相变理论的核心概念,如对称性断裂或机器学习中的临界点.以MNIST数据集的伊辛模型和自动编码器为例,说明了机器学习训练过程中的“相变”.这种介于机器学习和相变之间的新映射,为理解机器学习带来了新的方法,并使从物理角度解决机器学习问题成为可能.Phase transition is an important physical concept which represents the transformation from one thermodynamic state to another.It has a wide application in physics such as condensed matter physics,particle physics and astrophysics.Machine learning is the study of computer algorithms that improve automatically through experience.It is also a very active research field with the success of deep learning in recent years.This paper visually gives the evidence that the training process of supervised learning is quite similar to phase transition.Accordingly,it is possible to identify the central concepts of phase transition theory,such as symmetry breaking or critical point in machine learning.The Ising model and an autoencoder of the MNIST dataset are used as two examples to explain the“phase transition”in the training process of machine learning.This novel mapping between machine learning and phase transition brings a new method to understand machine learning and makes it possible to solve machine learning problems from a physical perspective.

关 键 词：相变 机器学习 伊辛模型 自动编码器 对称性断裂 

分 类 号：O157.4[理学—数学]