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ref: -2018 tags: machine learning manifold deep neural net geometry regularization date: 08-29-2018 14:30 gmt revision:0 [head]

LDMNet: Low dimensional manifold regularized neural nets.

  • Synopsis of the math:
    • Fit a manifold formed from the concatenated input ‘’and’’ output variables, and use this set the loss of (hence, train) a deep convolutional neural network.
      • Manifold is fit via point integral method.
      • This requires both SGD and variational steps -- alternate between fitting the parameters, and fitting the manifold.
      • Uses a standard deep neural network.
    • Measure the dimensionality of this manifold to regularize the network. Using a 'elegant trick', whatever that means.
  • Still yet he results, in terms of error, seem not very significantly better than previous work (compared to weight decay, which is weak sauce, and dropout)
    • That said, the results in terms of feature projection, figures 1 and 2, ‘’do’’ look clearly better.
    • Of course, they apply the regularizer to same image recognition / classification problems (MNIST), and this might well be better adapted to something else.
  • Not completely thorough analysis, perhaps due to space and deadlines.