Cortana will work offline? I didn't think something like this was possible, because I was sceptical whether standard smartphone was capable of all that natural language processing...
If I remember correctly they did mention the Offline part when they first revealed about Cortana. I think their plan is to do offline language processing with possible online cross checks where cellular internet service is either terrible or nonexistent. So in parts of Asia where cellular internet is slow, it wouldn't appear laggy.
I seriously doubt that Microsoft has such advanced language processing capabilities that can work offline on a smartphone. For example, as of a year ago, Xbox speed recognition was still based on an ancient technology derived from Tellme networks, you can see it by yourself during Xbox One voice recognition demos. And now you're saying that phone has more processing power to do that better than a full blown gaming console?