Solving ODE with Universal Flows: Approximation Theory for Flow-Based ModelsDownload PDF

26 Feb 2020 (modified: 26 Apr 2020)ICLR 2020 Workshop DeepDiffEq Blind SubmissionReaders: Everyone
  • Keywords: Normalizing flows, ODE, neural ODE, universal approximation
  • TL;DR: We we invertible neural networks to approximate solutions to ODEs to show they are universal density approximators.
  • Abstract: Normalizing flows are powerful invertible probabilistic models that can be used to translate two probability distributions, in a way that allows us to efficiently track the change of probability density. However, to trade for computational efficiency in sampling and in evaluating the log-density, special parameterization designs have been proposed at the cost of representational expressiveness. In this work, we propose to use ODEs as a framework to establish universal approximation theory for certain families of flow-based models.
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