Neural network pruning reduces the computational cost of an over-parameterized network to improve its efficiency. Popular methods vary from $\ell_1$-norm sparsification to Neural Architecture Search (NAS).

In this work, we propose a novel pruning method that optimizes the final accuracy of the pruned network and distills knowledge from the over-parameterized parent network's inner layers. To enable this approach, we formulate the network pruning as a Knapsack Problem which optimizes the trade-off between the importance of neurons and their associated computational cost.

Then we prune the network channels while maintaining the high-level structure of the network. The pruned network is fine-tuned under the supervision of the parent network using its inner network knowledge, a technique we refer to as the Inner Knowledge Distillation.

Our method leads to state-of-the-art pruning results on ImageNet, CIFAR-10 and CIFAR-100 using ResNet backbones. To prune complex network structures such as convolutions with skip-links and depth-wise convolutions, we propose a block grouping approach to cope with these structures.

Through this we produce compact architectures with the same FLOPs as EfficientNet-B0 and MobileNetV3 but with higher accuracy, by $1\%$ and $0.3\%$ respectively on ImageNet, and faster runtime on GPU.