HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference

Jakob Kruse, Gianluca Detommaso, Robert Scheichl, Ullrich Köthe

Research output: Contribution to journalArticlepeer-review

10 Citations (SciVal)


A large proportion of recent invertible neural architectures is based on a coupling block design. It operates by dividing incoming variables into two sub-spaces, one of which parameterizes an easily invertible (usually affine) transformation that is applied to the other. While the Jacobian of such a transformation is triangular, it is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that (affine) coupling can be repeated recursively within the resulting sub-spaces, leading to an efficiently invertible block with dense triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We demonstrate the power of our method for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.
Original languageEnglish
Pages (from-to)8191-8199
JournalProceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI-21)
Issue number9
Publication statusPublished - 18 May 2021


  • stat.ML
  • cs.AI
  • cs.LG


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