Invariant scattering convolution networks

Joan Bruna, Stephane Mallat

Research output: Contribution to journalArticlepeer-review


A wavelet scattering network computes a translation invariant image representation which is stable to deformations and preserves high-frequency information for classification. It cascades wavelet transform convolutions with nonlinear modulus and averaging operators. The first network layer outputs SIFT-type descriptors, whereas the next layers provide complementary invariant information that improves classification. The mathematical analysis of wavelet scattering networks explains important properties of deep convolution networks for classification. A scattering representation of stationary processes incorporates higher order moments and can thus discriminate textures having the same Fourier power spectrum. State-of-the-art classification results are obtained for handwritten digits and texture discrimination, with a Gaussian kernel SVM and a generative PCA classifier.

Original languageEnglish (US)
Article number6522407
Pages (from-to)1872-1886
Number of pages15
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number8
StatePublished - 2013


  • Classification
  • convolution networks
  • deformations
  • invariants
  • wavelets

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


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