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The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in latent space are associated with the quality of the underlying generative model. In this paper, we show that not all such interpolations are comparable as they can deviate arbitrarily from the shortest interpolation curve given by the geodesic. This deviation is revealed by computing curve lengths with the pull-back metric of the generative model, finding shorter curves than the straight line between endpoints, and measuring a non-zero relative length improvement on this straight line. This leads to a strategy to compare linear interpolations across two generative models. We also show the effect and importance of choosing an appropriate output space for computing shorter curves. For this computation we derive an extension of the pull-back metric.
Unsupervised meta-learning approaches rely on synthetic meta-tasks that are created using techniques such as random selection, clustering and/or augmentation. Unfortunately, clustering and augmentation are domain-dependent, and thus they require eith
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be impo
Generative Adversarial networks (GANs) have obtained remarkable success in many unsupervised learning tasks and unarguably, clustering is an important unsupervised learning problem. While one can potentially exploit the latent-space back-projection i
Kernel PCA is a powerful feature extractor which recently has seen a reformulation in the context of Restricted Kernel Machines (RKMs). These RKMs allow for a representation of kernel PCA in terms of hidden and visible units similar to Restricted Bol
We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural net