matrix and if you take the x here to be the key matrix then this is equivalent to the update or sorry the attention mechanism of a modern transformer so that's the point of the paper is that we can look at the transformer attention mechanism as a hopfield network and they have this interesting this interesting diagram at the end right here uh so the appendix you know this is typical i guess sep ho haita i remember this sailor paper had like 60 pages of machine proof appendix this also this has like 70 page appendix