Latent Space Oddity: on the Curvature of Deep Generative Models
This work addresses a foundational issue in deep generative models, improving their geometric understanding and practical performance, though it is incremental in building on existing frameworks.
The paper tackled the problem of distortion in the latent spaces of deep generative models by characterizing it with a stochastic Riemannian metric, which improved distances, interpolants, probability distributions, sampling, and clustering, and proposed a new generator architecture that vastly improved variance estimates, as demonstrated on convolutional and fully connected variational autoencoders.
Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator imply that the latent space gives a distorted view of the input space. Under mild conditions, we show that this distortion can be characterized by a stochastic Riemannian metric, and demonstrate that distances and interpolants are significantly improved under this metric. This in turn improves probability distributions, sampling algorithms and clustering in the latent space. Our geometric analysis further reveals that current generators provide poor variance estimates and we propose a new generator architecture with vastly improved variance estimates. Results are demonstrated on convolutional and fully connected variational autoencoders, but the formalism easily generalize to other deep generative models.