  Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix
factorization algorithms in that it does not make a low rank assumption. This
makes MMF especially well suited to modeling certain types of graphs with
complex multiscale or hierarchical strucutre. While MMF promises to yields a
useful wavelet basis, finding the factorization itself is hard, and existing
greedy methods tend to be brittle. In this paper we propose a learnable version
of MMF that carfully optimizes the factorization with a combination of
reinforcement learning and Stiefel manifold optimization through
backpropagating errors. We show that the resulting wavelet basis far
outperforms prior MMF algorithms and provides the first version of this type of
factorization that can be robustly deployed on standard learning tasks.
