Rayleigh EigenDirections (REDs): Nonlinear GAN Latent Space Traversals for Multidimensional Features.

We present a method for finding paths in a deep generative model's latent space that can maximally vary one set of image features while holding others constant. Crucially, unlike past traversal approaches, ours can manipulate arbitrary multidimensional features of an image such as facial identity and pixels within a specified region. Our method is principled and conceptually simple: optimal traversal directions are chosen by maximizing differential changes to one feature set such that changes to another set are negligible. We show that this problem is nearly equivalent to one of Rayleigh quotient maximization, and provide a closed-form solution to it based on solving a generalized eigenvalue equation. We use repeated computations of the corresponding optimal directions, which we call Rayleigh EigenDirections (REDs), to generate appropriately curved paths in latent space. We empirically evaluate our method using StyleGAN2 and BigGAN on the following image domains: faces, living rooms and ImageNet. We show that our method is capable of controlling various multidimensional features: face identity, geometric and semantic attributes, spatial frequency bands, pixels within a region, and the appearance and position of an object. Our work suggests that a wealth of opportunities lies in the local analysis of the geometry and semantics of latent spaces.