On the Convergence Rate of Gaussianization with Random Rotations
This addresses a scalability issue for Gaussianization, an incremental improvement in generative modeling for low-dimensional data.
The paper tackles the slowdown of Gaussianization's convergence speed in high dimensions, showing analytically that the number of layers scales linearly with dimension for Gaussian input and observing similar empirical trends for arbitrary distributions.
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.