Top eigenvectors of A^T A of a pretrained GAN generator's first affine layer are linear latent directions that edit semantic attributes

Shen & Zhou take the unit directions n maximizing ||An||^2 for the first affine layer y = Az + b of a pretrained generator, i.e. the top eigenvectors of A^T A, as semantic directions in the latent space, with no sampling or training [shen-zhou-2021-sefa] Shifting the latent code as z + alpha*n edits attributes; on PGGAN (CelebA-HQ) the re-scoring diagonal is 0.51 (pose), 0.55 (gender) and 0.34 (age), while SeFa fails to find an eyeglasses direction and the gender/age directions show cross-attribute change (0.46 on the gender row's age entry) [shen-zhou-2021-sefa] Against GANSpace on StyleGAN (FFHQ), attribute re-scoring is 0.38 vs 0.33 and 59% of user-study votes favour SeFa [shen-zhou-2021-sefa] Restricting the factorization to bottom, middle or top layers of StyleGAN/StyleGAN2 gives directions the paper describes as organized as a hierarchy (e.g. for cars bottom layers rotation, middle layers shape, top layers color) [shen-zhou-2021-sefa]