  Convolutional neural networks (CNNs) are reported to be overparametrized. The
search for optimal (minimal) and sufficient architecture is an NP-hard problem
as the hyperparameter space for possible network configurations is vast. Here,
we introduce a layer-by-layer data-driven pruning method based on the
mathematical idea aiming at a computationally-scalable entropic relaxation of
the pruning problem. The sparse subnetwork is found from the pre-trained (full)
CNN using the network entropy minimization as a sparsity constraint. This
allows deploying a numerically scalable algorithm with a sublinear scaling
cost. The method is validated on several benchmarks (architectures): (i) MNIST
(LeNet) with sparsity 55%-84% and loss in accuracy 0.1%-0.5%, and (ii) CIFAR-10
(VGG-16, ResNet18) with sparsity 73-89% and loss in accuracy 0.1%-0.5%.
