Fourier transform in Machine Learning

An example would be training large convolutional neural nets. For example, see: Fast Training of Convolutional Networks through FFTs (Mathieu et al. 2013) Another application is sparse signal processing, where the goal is to approximate a signal as a sparse linear combination of basis functions from a'signal dictionary'. The link here is that the set of sinusoids are, of course, a good dictionary for signals that are sparse in the Fourier domain. If I recall correctly, Fourier dictionaries show up in this literature.