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. Code available at: https://github.com/mmichelis/GenerativeLatentSpace

With the advent of Artificial Intelligence and new manufacturing techniques, Autonomous Underwater Vehicles (AUVs) have started to prevail over their manned version in terms of cost efficiency when it comes to accomplish tasks in ocean exploration, offshore platform and ship maintenance or other military missions. As progress has been made over the past years, autonomy remains a topical issue for the untethered AUVs. Drawing its inspiration from nature, this paper aims at minimizing the energy consumed by the device on a specific mission by allowing its shape, parameterized with Bezier curves, to morph throughout time. The framework is restricted to one dimensional trajectories only. A first step consisting of finding the optimal velocity and shapes added mass coefficient in surge as functions of time for a given mission is presented. Then a way of determining the succession of shapes the AUV must take so that it has the right added mass coefficient at any time is proved and used. This last part is made computationally affordable by using a Neural Network instead of a Boundary Element Method to evaluate the hydrodynamic coefficient in surge of the shape. Outliers detection and elimination are being performed on the training dataset to increase the predictive model reliability and robustness.