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%.
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