拉回信息几何
Pulling back information geometry
摘要：
潜空间几何学已经证明了它为与深层生成模型的潜变量交互提供了一个丰富而严格的框架。然而，现有的理论依赖于解码器是高斯分布，因为其简单的重新参数化允许我们将生成过程解释为确定性流形的随机投影。因此，当应用于不容易重新参数化的解码器时，这种方法会失败。我们在这里建议使用与解码器分布空间相关的Fisher-Rao度量作为参考度量，我们将其拉回到潜在空间。我们表明，我们可以实现有意义的潜在的几何形状为广泛的解码器的分布，以前的理论是不适用的，打开大门的“黑盒”潜在的几何形状。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
