Image variation in several real pretrained GANs concentrates along surprisingly few, position-homogeneous major axes of the pullback metric

A Riemannian pullback metric is eigen-decomposed at sampled latent positions across several real pretrained GANs, including BigGAN-deep (class-conditional, ImageNet), PGGAN (CelebA) and StyleGAN2 (FFHQ) [wang-ponce-2021-geometry-of-deep-generative-image-models] Image variation around each latent position is concentrated along surprisingly few major axes of the pullback metric (highly anisotropic), rather than spread evenly across all latent dimensions [wang-ponce-2021-geometry-of-deep-generative-image-models] The dominant axes are similar across different positions in latent space (homogeneous), and the top eigenvectors correspond to interpretable, reusable image transforms [wang-ponce-2021-geometry-of-deep-generative-image-models]