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A data processing system having a neural network architecture for receiving a binary network input and, in dependence on the binary network input, propagating signals via a plurality of processing nodes, in accordance with respective binary weights, to form a network output, the data processing system being configured to train a node by implementing an error correcting function to identify a set of binary weights which minimize, for a given input to the node, any error between an output of the node when formed in accordance with current binary weights of the node and a preferred output from the node and to update the binary weights of the node to be the identified weights. This training is performed without storing and/or using any higher arithmetic precision weights or other components.