Alternatives to the Scaled Dot Product for Attention in the Transformer Neural Network Architecture

The transformer neural network architecture uses a form of attention in which the dot product of query and key is divided by the square root of the key dimension before applying softmax. This scaling of the dot product is designed to avoid the absolute value of the dot products becoming so large that applying softmax leads to vanishing gradients. In this paper, we propose some alternative scalings, including dividing the dot product instead by the sum of the key lengths before applying softmax. We use simulated keys and queries to show that in many situations this appears to be more effective at avoiding regions where applying softmax leads to vanishing gradients.