Many researchers are using neural network to infer embedding vectors for words, users, or items. Word embeddings, e.g., word2vec, allow people to calculate sum, average, and difference over embeddings.
So does it make sense to multiply two embeddings? For instance, one 200-d user embedding and one 200-d movies embedding. The miltiplication results in a new 200-d vector, which should be able to represent the interaction of the user and the movie. The new vector can be an input of any prediction model. Does it make sense?