  The wavelet scattering transform creates geometric invariants and deformation
stability. In multiple signal domains, it has been shown to yield more
discriminative representations compared to other non-learned representations
and to outperform learned representations in certain tasks, particularly on
limited labeled data and highly structured signals. The wavelet filters used in
the scattering transform are typically selected to create a tight frame via a
parameterized mother wavelet. In this work, we investigate whether this
standard wavelet filterbank construction is optimal. Focusing on Morlet
wavelets, we propose to learn the scales, orientations, and aspect ratios of
the filters to produce problem-specific parameterizations of the scattering
transform. We show that our learned versions of the scattering transform yield
significant performance gains in small-sample classification settings over the
standard scattering transform. Moreover, our empirical results suggest that
traditional filterbank constructions may not always be necessary for scattering
transforms to extract effective representations.
