  In this report we present a new model of concepts, based on the framework of
variational autoencoders, which is designed to have attractive properties such
as factored conceptual domains, and at the same time be learnable from data.
The model is inspired by, and closely related to, the Beta-VAE model of
concepts, but is designed to be more closely connected with language, so that
the names of concepts form part of the graphical model. We provide evidence
that our model -- which we call the Conceptual VAE -- is able to learn
interpretable conceptual representations from simple images of coloured shapes
together with the corresponding concept labels. We also show how the model can
be used as a concept classifier, and how it can be adapted to learn from fewer
labels per instance. Finally, we formally relate our model to Gardenfors'
theory of conceptual spaces, showing how the Gaussians we use to represent
concepts can be formalised in terms of "fuzzy concepts" in such a space.
