Interpreting variational autoencoders with fuzzy logic: A step towards interpretable deep learning based fuzzy classifiers

The emerging success of Deep Learning (DL) in various application areas comes also with the questions starting with "How"s and "Why"s. These questions can be answered if the DL methods are interpretable and thus provide a certain a degree of explanation. In this paper, we propose a DL framework that leverages the advantages of β-Variational Autoencoder (VAE) and Fuzzy Sets (FSs), which are disentanglement and linguistic representation, for the design of a novel DL based Fuzzy Classifier (FC). We first present a step-by-step design approach to construct the DL-FC which is composed of the encoder layer of β-VAE and a Fuzzy Logic System (FLS) followed by a softmax layer. The β-VAE is trained so that the semantic information of the high dimensional data is captured. The latent space of the β-VAE is clustered to extract FSs. The FSs are then used to define antecedents of the FLS that is trained with DL methods. We present results conducted on the MNIST dataset and showed that DL-FC is quite competitive with its deep neural network counterpart. We then try to provide an interpretation to the antecedents of FLS by examining the FSs, the latent traversals and heat-maps of each latent dimension. The results show that the antecedents of FLS can be defined with linguistic interpretations. Thus, for the first time in the literature, we showed that linguistic interpretations can be defined for the latent space of β-VAE with FSs.