Wrapped Normal Distribution in Kinematic SpaceDownload PDF


09 Jul 2020 (modified: 09 Jul 2020)OpenReview Anonymous Preprint Blind SubmissionReaders: Everyone
  • Keywords: Deep Representation Learning, pseudo-Riemannian Manifolds, Kinematic Space
  • TL;DR: We introduce a novel geometrical space called Kinematic Space and assess its efficacy as geometrical inductive for deep representation learning.
  • Abstract: In this paper, we introduce a new auxiliary Lorentzian space called Kinematic Space, as a geometrical inductive for deep representation learning. Using the non-Euclidean realm for learning representations has gained traction due to their general appeal of handling anatomically hierarchical data. We propose a Gaussian-like distribution that is compatible with gradient-based learning methods and as an application, we formulate a Kinematic space analog of Variational Auto Encoder called $\mathcal{K}_s$-VAE which uses Gaussian-like priors to learn latent representations in our prescribed geometry. We perform experiments on binarized MNIST dataset and report log-likelihood as our evaluation metric. Our experiments are evidentiary for the utility of Kinematic Space in machine learning pipelines.
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