Parametric Scattering Networks.

The wavelet scattering transform creates geometric invariants and deformation stability from an initial structured signal. 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. Focusing on Morlet wavelets, we propose to instead adapt the scales, orientations, and slants of the filters to produce problem-specific parametrizations of the scattering transform. We show that our learned versions of the scattering transform yield significant performance gains over the standard scattering transform in the small sample classification settings, and our empirical results suggest that tight frames may not always be necessary for scattering transforms to extract effective representations.