A real trained importance-weighted autoencoder's pullback-Riemannian geodesics outperform Euclidean latent interpolation on MNIST, a simulated robot arm, and real human motion-capture data

A deterministic generator-Jacobian pullback Riemannian metric, smoothed via SVD regularization, is computed on the fixed 2D latent space of real importance-weighted autoencoders (IWAEs) independently trained on real binarized MNIST digits, a simulated 6-degree-of-freedom KUKA robot-arm circular-motion dataset, and real CMU human motion-capture walking data [chen-etal-2018-metrics-for-deep-generative-models] On MNIST, the geodesic between two digit-class latents (path length 62.9) crosses only two digit classes and follows the data manifold, versus a Euclidean interpolation (length 74.3) that crosses four classes and produces less smooth reconstructions [chen-etal-2018-metrics-for-deep-generative-models] On the simulated robot arm, the geodesic (length 0.54) produces smooth, natural end-effector motion without explicit task-space constraints, far outperforming Euclidean interpolation (length 1.48); on real motion-capture walking data the geodesic (2.57) again outperforms Euclidean interpolation (2.89), avoiding large body-pose jumps that occur when the Euclidean path crosses high-magnification-factor latent regions [chen-etal-2018-metrics-for-deep-generative-models]