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Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory, researchers have concentrated on designing compression methods in order to make them practical for constrained platforms. In this paper, we propose an approach of partial regularization rather than the original form of penalizing all parameters, which is said to be full regularization, to conduct model compression at a higher speed. It is reasonable and feasible according to the existence of the permutation invariant property of neural networks. Experimental results show that as we expected, the computational complexity is reduced by observing less running time in almost all situations. It should be owing to the fact that partial regularization method invovles a lower number of elements for calculation. Surprisingly, it helps to improve some important metrics such as regression fitting results and classification accuracy in both training and test phases on multiple datasets, telling us that the pruned models have better performance and generalization ability. What's more, we analyze the results and draw a conclusion that an optimal network structure must exist and depend on the input data.