Systems, methods, and apparatus, including computer programs encoded on a computer storage medium, related to associative long short-term memory (LSTM) neural network layers configured to maintain N copies of an internal state for the associative LSTM layer, N being an integer greater than one. In one aspect, a system includes a recurrent neural network including an associative LSTM layer, wherein the associative LSTM layer is configured to, for each time step, receive a layer input, update each of the N copies of the internal state using the layer input for the time step and a layer output generated by the associative LSTM layer for a preceding time step, and generate a layer output for the time step using the N updated copies of the internal state.