The linear transformations in converged deep networks show fast eigenvalue decay. The distribution of eigenvalues looks like a Heavy-tail distribution, where the vast majority of eigenvalues is small, but not actually zero, and only a few spikes of large eigenvalues exist.
 We use a stochastic approximator to generate histograms of eigenvalues. This allows us to investigate layers with hundreds of thousands of dimensions. We show how the distributions change over the course of image net training, converging to a similar heavy-tail spectrum across all intermediate layers. Understanding the structure in the linear transformations might be an important aspect of understanding generalization in deep networks. To this end we have presented a stochastic approach that allows us to estimate the eigenvalue spectrum of these transformations. We show how the spectrum evolves during imagenet training using convolutional networks, more specifically squeeze_net networks.In the future we want to apply similar approaches to estimating the covariance structure of the intermediate feature representations and investigate the relations between covariance matrices and parameter matrices. Since the estimator we use is differentiable BID5 BID0 , it may be interesting to investigate its usefulness for regularization.
We investigate the eigenvalues of the linear layers in deep networks and show that the distributions develop heavy-tail behavior during training.
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