2016/08/31 by Haiping Huang, Taro Toyoizumi · 20 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Competitive learning #Computer science #Deep learning #Entropy (arrow of time) #Feature (linguistics) #Feature learning #Machine Learning in Materials Science #Machine learning #Message passing #Pattern recognition (psychology) #Physics #Restricted Boltzmann machine #Salient #Semi-supervised learning #Statistical Mechanics and Entropy #Theoretical and Computational Physics #Unsupervised learning #cond-mat.dis-nn #cond-mat.stat-mech #cs.LG #q-bio.NC
paper · pdf · doi:10.1103/physreve.94.062310
published in Physical review. E 94(6), 062310 (American Physical Society) · 8 pages, 7 figures (5 pages, 4 figures in the main text and 3 pages of appendix)
arxiv created 2016/11/11 · openalex publication_date 2016/12/21 · arxiv updated 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Unsupervised neural network learning extracts hidden features from unlabeled training data. This is used as a pretraining step for further supervised learning in deep networks. Hence, understanding unsupervised learning is of fundamental importance. Here, we study the unsupervised learning from a finite number of data, based on the restricted Boltzmann machine where only one hidden neuron is considered. Our study inspires an efficient message-passing algorithm to infer the hidden feature and estimate the entropy of candidate features consistent with the data. Our analysis reveals that the learning requires only a few data if the feature is salient and extensively many if the feature is weak. Moreover, the entropy of candidate features monotonically decreases with data size and becomes negative (i.e., entropy crisis) before the message passing becomes unstable, suggesting a discontinuous phase transition. In terms of convergence time of the message-passing algorithm, the unsupervised learning exhibits an easy-hard-easy phenomenon as the training data size increases. All these properties are reproduced in an approximate Hopfield model, with an exception that the entropy crisis is absent, and only continuous phase transition is observed. This key difference is also confirmed in a handwritten digits dataset. This study deepens our understanding of unsupervised learning from a finite number of data and may provide insights into its role in training deep networks.