Abstract
With the unprecedented performance achieved by deep learning, it is commonly believed that deep neural networks (DNNs) attempt to extract informative features for learning tasks. To formalize this intuition, we apply the local information geometric analysis and establish an information-theoretic framework for feature selection, which demonstrates the information-theoretic optimality of DNN features. Moreover, we conduct a quantitative analysis to characterize the impact of network structure on the feature extraction process of DNNs. Our investigation naturally leads to a performance metric for evaluating the effectiveness of extracted features, called the H-score, which illustrates the connection between the practical training process of DNNs and the information-theoretic framework. Finally, we validate our theoretical results by experimental designs on synthesized data and the ImageNet dataset.
Highlights
Due to the striking performance of deep learning in various application fields, deep neural networks (DNNs) have gained great attention in modern computer science
This paper aims to provide an information-theoretic interpretation to the feature extraction process in DNNs, to bridge the gap between the practical deep learning implementations and information-theoretic characterizations
The local information geometric method is closely related to the conventional Hirschfeld– Gebelein–Rényi (HGR) maximal correlation [25,26,27] problem, which has attracted increasing interest in the information theory community [28,29,30,31,32,33], and has been applied in data analysis [34] and privacy studies [35]
Summary
Due to the striking performance of deep learning in various application fields, deep neural networks (DNNs) have gained great attention in modern computer science. The understanding of the feature extraction behind these models is relatively lacking, which poses challenges for their application in security-sensitive tasks, such as the autonomous vehicle To address this problem, there have been numerous research efforts, including both experimental and theoretical studies [6]. The experimental studies usually focus on some empirical properties of the feature extracted by DNNs, by visualizing the feature [7] or testing its performance on specific training settings [8] or learning tasks [9]. Though such empirical methods have provided some intuitive interpretations, the performance can highly depend on the data and network architecture used. While the feature visualization works well on convolutional neural networks, its application to other networks is typically less effective [10]
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