On the Convergence Rate of Gaussianization with Random Rotations
Felix Draxler, Lars Kühmichel, Armand Rousselot, Jens Müller, Christoph Schnoerr, Ullrich Koethe
Abstract
Gaussianization is a simple generative model that can be trained without backpropagation. It has shown compelling performance on low dimensional data. As the dimension increases, however, it has been observed that the convergence speed slows down. We show analytically that the number of required layers scales linearly with the dimension for Gaussian input. We argue that this is because the model is unable to capture dependencies between dimensions. Empirically, we find the same linear increase in cost for arbitrary input $p(x)$, but observe favorable scaling for some distributions. We explore potential speed-ups and formulate challenges for further research.
BibTeX
@inproceedings{icml2023_ontheconvergence,
title = {On the Convergence Rate of Gaussianization with Random Rotations},
author = {Felix Draxler and Lars Kühmichel and Armand Rousselot and Jens Müller and Christoph Schnoerr and Ullrich Koethe},
booktitle = {ICML 2023},
year = {2023}
}