Cosine Normalization: Using Cosine Similarity Instead of Dot Product in Neural Networks
This addresses the issue of internal covariate shift and generalization in neural networks for researchers and practitioners, but it is incremental as it builds on existing normalization methods.
The paper tackled the problem of unbounded dot product in neural networks causing large variance and poor generalization by proposing cosine normalization, which uses cosine similarity instead of dot product. Experiments on datasets like MNIST and CIFAR-10/100 showed that cosine normalization achieves better performance than other normalization techniques, with specific gains reported.
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 or centered cosine similarity (Pearson Correlation Coefficient) instead of dot product in neural networks, which we call cosine normalization. We compare cosine normalization with batch, weight and layer normalization in fully-connected neural networks as well as convolutional networks on the data sets of MNIST, 20NEWS GROUP, CIFAR-10/100 and SVHN. Experiments show that cosine normalization achieves better performance than other normalization techniques.