MD-LSM: An Efficient Tool for Real-time Monitoring Linear Separability of Hidden-layer Outputs of Deep Networks

Chao Zhang, Xinyu Chen, Wensheng Li, Xingwu Liu, Dacheng Tao

Keywords: linear separability, deep network, hidden layer, Minkowski difference

TL;DR: This paper provides a new tool for understanding the working mechanism of deep networks.

Abstract: Many studies have shown that evaluating the linear separability of hidden-layer outputs plays a key role in understanding the working mechanism of deep networks. However, it is still challenging to develop the linear separability measure (LSM) that satisfies all of the following requirements: 1) it should be an absolute measure; 2) it should be insensitive to the outliers; and 3) its computational cost should be low for real-time monitoring the behavior of each hidden layer. In this paper, we propose the Minkowski difference-based linear separability measures (MD-LSMs) that just meet the first two requirements. Moreover, we also introduce an approximate calculation method to significantly decrease their computation costs with only a slight precision sacrifice. As an application example, we conduct the experiments on the real-time monitoring for the hidden-layer behaviors of several popular deep networks, and show that the outputs of the hidden layers adjacent to the output layer have higher linear separability degrees. We also observe that the change of linear separability degree of hidden layers (especially the ones are adjacent to the output layers) are in sync with the change of the training accuracy of the entire network. It implies that the linear separability of some important hidden layers can be treated as a performance criterion to characterize the network's training behavior. The relevant theoretical discussion also validates this finding.

Primary Area: interpretability and explainable AI

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Submission Number: 4139