To initialize the m-dimensional domain embeddings ed new , we use the column-wise average of all utterance vectors in the training datah avg , and project it to the domain embedding space using a matrix U ∈ R m×m .
the parameters of U * are learned using the column-wise average utterance vectorsh avg j and learned domain vectors for all existing domains d j this is a write-to-memory operation that creates a new domain representation after attending to all existing domain representations.