4,514 research outputs found
The Riemannian Geometry of Deep Generative Models
Deep generative models learn a mapping from a low dimensional latent space to
a high-dimensional data space. Under certain regularity conditions, these
models parameterize nonlinear manifolds in the data space. In this paper, we
investigate the Riemannian geometry of these generated manifolds. First, we
develop efficient algorithms for computing geodesic curves, which provide an
intrinsic notion of distance between points on the manifold. Second, we develop
an algorithm for parallel translation of a tangent vector along a path on the
manifold. We show how parallel translation can be used to generate analogies,
i.e., to transport a change in one data point into a semantically similar
change of another data point. Our experiments on real image data show that the
manifolds learned by deep generative models, while nonlinear, are surprisingly
close to zero curvature. The practical implication is that linear paths in the
latent space closely approximate geodesics on the generated manifold. However,
further investigation into this phenomenon is warranted, to identify if there
are other architectures or datasets where curvature plays a more prominent
role. We believe that exploring the Riemannian geometry of deep generative
models, using the tools developed in this paper, will be an important step in
understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page
3D Point Capsule Networks
In this paper, we propose 3D point-capsule networks, an auto-encoder designed
to process sparse 3D point clouds while preserving spatial arrangements of the
input data. 3D capsule networks arise as a direct consequence of our novel
unified 3D auto-encoder formulation. Their dynamic routing scheme and the
peculiar 2D latent space deployed by our approach bring in improvements for
several common point cloud-related tasks, such as object classification, object
reconstruction and part segmentation as substantiated by our extensive
evaluations. Moreover, it enables new applications such as part interpolation
and replacement.Comment: As published in CVPR 2019 (camera ready version), with supplementary
materia
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