ProtoGMVAE: A Variational Auto-Encoder with True Gaussian Mixture Prior for Prototypical-based Self-Explainability

Recently, significant efforts were made towards Variational Autoencoder (VAE) -based prototypical Self Explainable Models (SEM) for image classification. The princi-ple is to learn class-specific prototypes that can be projected back into the image spacethanks to the decoding branch of a VAE. However, existing VAE-based SEM fail to rep-resent properly the distribution of training samples in the embedding space, requiringto define specific additional constraints as diversity or orthogonality. In this work, wepropose to define the prototypes as the components of a Gaussian Mixture VAE (GM-VAE) that is an approximation of the distribution of training samples. We show that thisdefinition allows to produce relevant and diverse prototypes providing a probabilistic ex-planation of the model without assigning prototypes to a specific class. We support ourdefinition with extensive experimentation and comparison with previous self-explainableapproaches.