  Various forms of representations may arise in the many layers embedded in
deep neural networks (DNNs). Of these, where can we find the most compact
representation? We propose to use a pruning framework to answer this question:
How compact can each layer be compressed, without losing performance? Most of
the existing DNN compression methods do not consider the relative
compressibility of the individual layers. They uniformly apply a single target
sparsity to all layers or adapt layer sparsity using heuristics and additional
training. We propose a principled method that automatically determines the
sparsity of individual layers derived from the importance of each layer. To do
this, we consider a metric to measure the importance of each layer based on the
layer-wise capacity. Given the trained model and the total target sparsity, we
first evaluate the importance of each layer from the model. From the evaluated
importance, we compute the layer-wise sparsity of each layer. The proposed
method can be applied to any DNN architecture and can be combined with any
pruning method that takes the total target sparsity as a parameter. To validate
the proposed method, we carried out an image classification task with two types
of DNN architectures on two benchmark datasets and used three pruning methods
for compression. In case of VGG-16 model with weight pruning on the ImageNet
dataset, we achieved up to 75% (17.5% on average) better top-5 accuracy than
the baseline under the same total target sparsity. Furthermore, we analyzed
where the maximum compression can occur in the network. This kind of analysis
can help us identify the most compact representation within a deep neural
network.
