Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators
Authors: Takeshi Teshima, Isao Ishikawa, Koichi Tojo, Kenta Oono, Masahiro Ikeda, Masashi Sugiyama
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We answer this question by showing a convenient criterion: a CF-INN is universal if its layers contain affine coupling and invertible linear functions as special cases. As its corollary, we can affirmatively resolve a previously unsolved problem: whether normalizing flow models based on affine coupling can be universal distributional approximators. In the course of proving the universality, we prove a general theorem to show the equivalence of the universality for certain diffeomorphism classes, a theoretical insight that is of interest by itself. |
| Researcher Affiliation | Academia | Takeshi Teshima The University of Tokyo, RIKEN teshima@ms.k.u-tokyo.ac.jp Isao Ishikawa* Ehime University, RIKEN ishikawa.isao.zx@ehime-u.ac.jp Koichi Tojo RIKEN koichi.tojo@riken.jp Kenta Oono The University of Tokyo kenta_oono@mist.i.u-tokyo.ac.jp Masahiro Ikeda RIKEN masahiro.ikeda@riken.jp Masashi Sugiyama RIKEN, The University of Tokyo sugi@k.u-tokyo.ac.jp |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., specific repository link, explicit statement of code release) for the source code of the methodology described. |
| Open Datasets | No | The paper is theoretical and does not describe experiments that use training datasets. Therefore, it does not provide concrete access information for a publicly available or open dataset used for training. |
| Dataset Splits | No | The paper is theoretical and does not describe experiments that involve dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and does not describe experiments that would require specific hardware, therefore no hardware specifications are provided. |
| Software Dependencies | No | The paper is theoretical and does not mention specific ancillary software details with version numbers needed to replicate experiments. |
| Experiment Setup | No | The paper is theoretical and does not describe experiments, thus no experimental setup details like hyperparameters or training configurations are provided. |