quickly through them again theorems one and two deal with the convergence of this algorithm and the fact that it actually minimizes the proposed energy then theorem three says you can store exponentially many patterns in terms of the dimension of your space and theorems four and five say that this update rule will converge exponentially fast after after one step if you believe that and the retrieval error will also go down exponentially fast with the number of update steps that you do okay that sounds pretty pretty pretty