Neuron-level Structured Pruning using Polarization Regularizer

Neuron-level structured pruning is a very effective technique to reduce the computation of neural networks without compromising prediction accuracy. In previous works, structured pruning is usually achieved by imposing L1 regularization on the scaling factors of neurons, and pruning the neurons whose scaling factors are below a certain threshold. The reasoning is that neurons with smaller scaling factors have weaker influence on network output. A scaling factor close to 0 actually suppresses a neuron. However, L1 regularization lacks discrimination between neurons because it pushes all scaling factors towards 0. A more reasonable pruning method is to only suppress unimportant neurons (with 0 scaling factors) and simultaneously keep important neurons intact (with larger scaling factor). To achieve this goal, we propose a new regularizer on scaling factors, namely polarization regularizer. Theoretically, we prove that polarization regularizer pushes some scaling factors to 0 and others to a value $a > 0$. Experimentally, we show that structured pruning using polarization regularizer achieves much better results than using L1 regularizer. Experiments on CIFAR and ImageNet datasets show that polarization pruning achieves the state-of-the-art result to date.