• dotprod: Select negative examplesw in (4) according to a probability distribution derived from the vocabulary histogram proposed in <cite>[23]</cite> , but with the client thread supplied seed initializing the random number generation, and then return all partial dot products required to evaluate the gradient (4) for all positive output, negative output, and input word vectors associated with the minibatch, wherein the partial dot products involve those vector components stored on the designated shard: usv T s .