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Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to 'black box' latent geometries. * Equal contribution.Preprint. Under review.

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Update 1 Win rate: 0% Update 2 Win rate: 100% 0% 60% 100% Winrate Update 3 Win rate: 50%Fig. 1: Finding a level with the right difficulty via Intelligent Trial-and-Error (IT&E). IT&E [1]for games first creates a set of levels, arranged in a map that varies across level characteristics (amount of enemies and distance to goal). IT&E updates its beliefs about the difficulty of each level continuously using Gaussian Processes. In only three updates, the IT&E algorithm finds a level with ideal difficulty (win rate between 50%-70%) for a One Step Look-Ahead agent. The brighter the color in the maps, the closer the level is to the target difficulty, with darker colors representing levels that are either too easy or too hard.