On the Convergence Rate of Gaussianization with Random Rotations
Felix Draxler,u00a0Lars Ku00fchmichel,u00a0Armand Rousselot,u00a0Jens Mu00fcller,u00a0Christoph Schnoerr,u00a0Ullrich Koethe
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.
