Cosine Normalization: Using Cosine Similarity Instead of Dot Product in Neural Networks

Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change of input distribution, thus results in poor generalization, and aggravates the internal covariate shift which slows down the training. To bound dot product and decrease the variance, we propose to use cosine similarity instead of dot product in neural networks, which we call cosine normalization. Our experiments show that cosine normalization in fully-connected neural networks notably reduces the test err with lower divergence, compared to other normalization techniques. Applied to convolutional networks, cosine normalization also significantly enhances the accuracy of classification and accelerates the training.