  The impressive success of style-based GANs (StyleGANs) in high-fidelity image
synthesis has motivated research to understand the semantic properties of their
latent spaces. In this paper, we approach this problem through a geometric
analysis of latent spaces as a manifold. In particular, we propose a local
dimension estimation algorithm for arbitrary intermediate layers in a
pre-trained GAN model. The estimated local dimension is interpreted as the
number of possible semantic variations from this latent variable. Moreover,
this intrinsic dimension estimation enables unsupervised evaluation of
disentanglement for a latent space. Our proposed metric, called Distortion,
measures an inconsistency of intrinsic tangent space on the learned latent
space. Distortion is purely geometric and does not require any additional
attribute information. Nevertheless, Distortion shows a high correlation with
the global-basis-compatibility and supervised disentanglement score. Our work
is the first step towards selecting the most disentangled latent space among
various latent spaces in a GAN without attribute labels.
