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.

翻译：远方空间几何已经表明,它为与深层基因模型的潜在变量进行互动提供了丰富而严格的框架。然而,现有的理论依赖解码器作为高斯分布法,因为其简单的重新对称法使我们能够将生成过程解释为对确定性方块的随机投影。因此,这种方法在应用于不那么容易重新对称的解码器时会崩溃。我们在这里提议使用与解码器分布空间相关的Fisher-Rao指标作为参考指标,我们将其撤回到潜质空间。我们表明,我们可以为先前理论不适用的多种解码器分布法实现有意义的潜在潜在地理分布法,打开“黑盒”潜在几何体的大门。