StyleGAN2's W space is globally warped; local bases avoid traversal collapse

Choi et al. compute a Local Basis at each W-space point via SVD of the noise-to-W Jacobian, giving local principal-variation directions rather than one global set (as in GANSpace or SeFa) [choi-etal-2021-local-basis-gan-manifold] Grassmannian distance between top-k Local Basis subspaces shows nearby points are far more similar than random points, themselves distinct from a random-subspace null, so W space is globally warped rather than flat/affine [choi-etal-2021-local-basis-gan-manifold] Traversing along the Local Basis keeps FID low under strong perturbation while global methods' FID rises sharply (image collapse), a measured causal effect of respecting local geometry [choi-etal-2021-local-basis-gan-manifold]