title: Why Convolutional Networks Learn Oriented Bandpass Filters: A Hypothesis
abstract: It has been repeatedly observed that convolutional architectures when applied to
  image understanding tasks learn oriented bandpass filters. A standard explanation
  of this result is that these filters reflect the structure of the images that they have
  been exposed to during training: Natural images typically are locally composed
  of oriented contours at various scales and oriented bandpass filters are matched
  to such structure. The present paper offers an alternative explanation based not
  on the structure of images, but rather on the structure of convolutional architectures.
  In particular, complex exponentials are the eigenfunctions of convolution.
  These eigenfunctions are defined globally; however, convolutional architectures
  operate locally. To enforce locality, one can apply a windowing function to the
  eigenfunctions, which leads to oriented bandpass filters as the natural operators
  to be learned with convolutional architectures. From a representational point of
  view, these filters allow for a local systematic way to characterize and operate on
  an image or other signal.
authors: Richard P. Wildes
hIndex: Richard P. Wildes 35