Comparing the latent space of generative models

Different encodings of datapoints in the latent space of latent-vector generative models may result in more or less effective and disentangled characterizations of the different explanatory factors of variation behind the data. Many works have been recently devoted to the exploration of the latent space of specific models, mostly focused on the study of how features are disentangled and of how trajectories producing desired alterations of data in the visible space can be found. In this work we address the more general problem of comparing the latent spaces of different models, looking for transformations between them. We confined the investigation to the familiar and largely investigated case of generative models for the data manifold of human faces. The surprising, preliminary result reported in this article is that (provided models have not been taught or explicitly conceived to act differently) a simple linear mapping is enough to pass from a latent space to another while preserving most of the information. This is full of consequences for representation learning, potentially paving the way to the transformation of editing trajectories from one space to another, or the adaptation of disentanglement techniques between different generative domains.