Linear Time Complexity Deep Fourier Scattering Network and Extension to Nonlinear Invariants

Randall Balestriero, Herve Glotin

Abstract:

In this paper we propose a scalable version of a state-of-the-art deterministic time-
invariant feature extraction approach based on consecutive changes of basis and
nonlinearities, namely, the scattering network. The first focus of the paper is to
extend the scattering network to allow the use of higher order nonlinearities as
well as extracting nonlinear and Fourier based statistics leading to the required in-
variants of any inherently structured input. In order to reach fast convolutions and
to leverage the intrinsic structure of wavelets, we derive our complete model in the
Fourier domain. In addition of providing fast computations, we are now able to
exploit sparse matrices due to extremely high sparsity well localized in the Fourier
domain. As a result, we are able to reach a true linear time complexity with in-
puts in the Fourier domain allowing fast and energy efficient solutions to machine
learning tasks. Validation of the features and computational results will be pre-
sented through the use of these invariant coefficients to perform classification on
audio recordings of bird songs captured in multiple different soundscapes. In the
end, the applicability of the presented solutions to deep artificial neural networks
is discussed.

TL;DR: This paper proposes an extension of the Scattering Network in the Fourier domain and with nonlinear invariant computation for fast and scalable unsupervised representations

Conflicts: rice.edu, univ-tln.fr

Keywords: Unsupervised Learning, Applications, Deep learning