  Neural network compression empowers the effective yet unwieldy deep
convolutional neural networks (CNN) to be deployed in resource-constrained
scenarios. Most state-of-the-art approaches prune the model in filter-level
according to the "importance" of filters. Despite their success, we notice they
suffer from at least two of the following problems: 1) The redundancy among
filters is not considered because the importance is evaluated independently. 2)
Cross-layer filter comparison is unachievable since the importance is defined
locally within each layer. Consequently, we must manually specify layer-wise
pruning ratios. 3) They are prone to generate sub-optimal solutions because
they neglect the inequality between reducing parameters and reducing
computational cost. Reducing the same number of parameters in different
positions in the network may reduce different computational cost. To address
the above problems, we develop a novel algorithm named as COP
(correlation-based pruning), which can detect the redundant filters
efficiently. We enable the cross-layer filter comparison through global
normalization. We add parameter-quantity and computational-cost regularization
terms to the importance, which enables the users to customize the compression
according to their preference (smaller or faster). Extensive experiments have
shown COP outperforms the others significantly. The code is released at
https://github.com/ZJULearning/COP.
