Real CelebA- and SVHN-trained VAE manifolds are surprisingly close to zero curvature, so linear latent interpolation nearly matches true geodesics

Geodesic curves and parallel-transport algorithms are derived from a Riemannian pullback metric on the latent space of real convolutional VAEs (32-dimensional latent) trained on real CelebA and SVHN image data [shao-kumar-fletcher-2018-riemannian-geometry-deep-generative-models] The learned generator manifold is found to be surprisingly close to zero curvature, so that naive linear (Euclidean) interpolation paths in latent space closely approximate the true geodesics under the pullback metric [shao-kumar-fletcher-2018-riemannian-geometry-deep-generative-models] This is a notably different empirical emphasis from Arvanitidis, Hansen & Hauberg (2018)'s finding on other real VAEs that latent-space distortion is significant enough to require geodesic correction for good interpolation [shao-kumar-fletcher-2018-riemannian-geometry-deep-generative-models]