CNNs with Compact Activation Function

Activation function plays an important role in neural networks. We propose to use hat activation function, namely the first order B-spline, as activation function for CNNs including MgNet and ResNet. Different from commonly used activation functions like ReLU, the hat function has a compact support and no obvious spectral bias. Although spectral bias is thought to be beneficial for generalization, we show that MgNet and ResNet with hat function still exhibit a slightly better generalization performance than CNNs with ReLU function by our experiments of classification on MNIST, CIFAR10/100 and ImageNet datasets. This indicates that CNNs without spectral bias can have a good generalization capability. We also illustrate that although hat function has a small activation area which is more likely to induce vanishing gradient problem, hat CNNs with various initialization methods still works well.