How Does BN Increase Collapsed Neural Network Filters?

Improving sparsity of deep neural networks (DNNs) is essential for network compression and has drawn much attention. In this work, we disclose a harmful sparsifying process called filter collapse, which is common in DNNs with batch normalization (BN) and rectified linear activation functions (e.g. ReLU, Leaky ReLU). It occurs even without explicit sparsity-inducing regularizations such as $L_1$. This phenomenon is caused by the normalization effect of BN, which induces a non-trainable region in the parameter space and reduces the network capacity as a result. This phenomenon becomes more prominent when the network is trained with large learning rates (LR) or adaptive LR schedulers, and when the network is finetuned. We analytically prove that the parameters of BN tend to become sparser during SGD updates with high gradient noise and that the sparsifying probability is proportional to the square of learning rate and inversely proportional to the square of the scale parameter of BN. To prevent the undesirable collapsed filters, we propose a simple yet effective approach named post-shifted BN (psBN), which has the same representation ability as BN while being able to automatically make BN parameters trainable again as they saturate during training. With psBN, we can recover collapsed filters and increase the model performance in various tasks such as classification on CIFAR-10 and object detection on MS-COCO2017