Geometry of Deep Convolutional Networks

Sep 27, 2018 ICLR 2019 Conference Withdrawn Submission readers: everyone
  • Abstract: We give a formal procedure for computing preimages of convolutional network outputs using the dual basis defined from the set of hyperplanes associated with the layers of the network. We point out the special symmetry associated with arrangements of hyperplanes of convolutional networks that take the form of regular multidimensional polyhedral cones. We discuss the efficiency of of large number of layers of nested cones that result from incremental small size convolutions in order to give a good compromise between efficient contraction of data to low dimensions and shaping of preimage manifolds. We demonstrate how a specific network flattens a non linear input manifold to an affine output manifold and discuss it's relevance to understanding classification properties of deep networks.
  • Keywords: convolutional networks, geometry
  • TL;DR: Analysis of deep convolutional networks in terms of associated arrangement of hyperplanes
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