Local intrinsic dimension of a real StyleGAN2 latent manifold varies across latent space and correlates with disentanglement

Treating a real pretrained StyleGAN/StyleGAN2 generator's intermediate latent space as a Riemannian manifold, local intrinsic dimension is estimated at each sampled latent point via the generator's own local tangent-space structure [choi-etal-2023-local-intrinsic-dimension-gan-latent] Local intrinsic dimension varies substantially across the latent manifold rather than being constant, and is interpreted as the number of independent semantic variations available at that latent point [choi-etal-2023-local-intrinsic-dimension-gan-latent] A derived tangent-space-inconsistency metric (Distortion) correlates highly with supervised disentanglement scores despite requiring no attribute labels [choi-etal-2023-local-intrinsic-dimension-gan-latent]