We present a system for keyword spotting that, except for a frontend component for feature generation, it is entirely contained in a deep neural network (DNN) model trained "end-to-end" to predict the presence of the keyword in a stream of audio. The main contributions of this work are, first, an efficient memoized neural network topology that aims at making better use of the parameters and associated computations in the DNN by holding a memory of previous activations distributed over the depth of the DNN. The second contribution is a method to train the DNN, end-to-end, to produce the keyword spotting score. This system significantly outperforms previous approaches both in terms of quality of detection as well as size and computation.