Fast Approximate Geodesics for Deep Generative Models
This enables efficient similarity measurement in high-dimensional domains like images, but it is incremental as it builds on existing geodesic methods.
The paper tackles the computational complexity of computing geodesics in deep generative models by proposing a graph-based method that finds shortest paths using samples from the approximate posterior, achieving greatly reduced runtime without significant loss in quality, as validated on image datasets like Chair and FashionMNIST.
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the computational complexity of solving a non-convex optimisation problem. We propose finding shortest paths in a finite graph of samples from the aggregate approximate posterior, that can be solved exactly, at greatly reduced runtime, and without a notable loss in quality. Our approach, therefore, is hence applicable to high-dimensional problems, e.g., in the visual domain. We validate our approach empirically on a series of experiments using variational autoencoders applied to image data, including the Chair, FashionMNIST, and human movement data sets.