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

Analyzing the Latent Space of GAN through Local Dimension Estimation