A neural network training apparatus is described which has a network of worker nodes each having a memory storing a subgraph of a neural network to be trained. The apparatus has a control node connected to the network of worker nodes. The control node is configured to send training data instances into the network to trigger parallelized message passing operations which implement a training algorithm which trains the neural network. At least some of the message passing operations asynchronously update parameters of individual subgraphs of the neural network at the individual worker nodes.