Partially black-boxed collective interpretation and its application to SOM-based convolutional neural networks

摘要

This paper aims to extend collective interpretation to networks with complicated components. The collective interpretation is used to generate an internally interpretable model independently of specific inputs and learning conditions. The internally interpretable model is obtained by network compression where multi-layers are sequentially compressed, taking into account all possible routes from inputs to outputs. The network compression is easily applied to fully connected networks, but it cannot be applied to some networks with complicated components. Thus, to make the compression possible, we black-box partially and minimally these components to be replaced by the ordinary components. For demonstrating the effectiveness of this technique, we use here a new model based on the self-organizing map (SOM). Then, we introduce the convolutional neural networks (CNN) for dealing with SOM knowledge, usually represented in two-dimensional lattices. Because our network compression cannot deal with those convolutional components, we temporarily black-box the CNN components. Fixing the other connection weights, we re-train the partially black-boxed network to obtain the simplest prototype model for interpretation. The method was applied to two well-known data sets, and we demonstrated that the present method could compress the networks to get the simplest and interpretable ones. In addition, very stable compressed weights for interpretation could be obtained for easy interpretation. The results suggest that the main mechanism of multi-layered neural networks is based on linear relations between individual inputs and targets, to which peripheral non-linear ones are added. (c) 2021 Elsevier B.V. All rights reserved.