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.
CITATION STYLE
Chen, N., Ferroni, F., Klushyn, A., Paraschos, A., Bayer, J., & van der Smagt, P. (2019). Fast Approximate Geodesics for Deep Generative Models. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11728 LNCS, pp. 554–566). Springer Verlag. https://doi.org/10.1007/978-3-030-30484-3_45
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