  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 using metaheuristics,
specifically evolutionary algorithms and directed evolution, along with Stiefel
manifold optimization through backpropagating errors. We show that the
resulting wavelet basis far outperforms prior MMF algorithms and gives
comparable performance on standard learning tasks on graphs. Furthermore, we
construct the wavelet neural networks (WNNs) learning graphs on the spectral
domain with the wavelet basis produced by our MMF learning algorithm. Our
wavelet networks are competitive against other state-of-the-art methods in
molecular graphs classification and node classification on citation graphs. We
release our implementation at https://github.com/HySonLab/LearnMMF
