title: Linear Time Complexity Deep Fourier Scattering Network and Extension to Nonlinear Invariants
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.
authors: Randall Balestriero Herve Glotin
hIndex: Herve Glotin 32