Class-distinguishing latent regions of real disentangled VAE variants carry measurably higher pullback-metric curvature than a vanilla VAE's latent space
measured in 1 paperA Riemannian pullback metric is compared across a vanilla VAE and three disentangling-representation VAE variants (Szabo et al., Mathieu et al., and Jha et al.'s cycle-consistent VAE), all trained on real MNIST digits, MultiPIE faces and 3D Chairs data [shukla-etal-2018-geometry-of-deep-generative-models-disentangled-representations] Latent regions carrying class-distinguishing features exhibit measurably higher curvature under the pullback metric in the disentangled-representation models than in a vanilla VAE's latent space [shukla-etal-2018-geometry-of-deep-generative-models-disentangled-representations] Curvature-derived geodesic distances again improve interpolation quality relative to naive Euclidean latent distance, consistent with the same finding on other real VAEs [shukla-etal-2018-geometry-of-deep-generative-models-disentangled-representations]