Methods, systems, and apparatus, including computer programs encoded on computer storage media, for augmenting neural networks with an external memory. One of the systems includes a sparse memory access subsystem that is configured to perform operations comprising generating a sparse set of reading weights that includes a respective reading weight for each of the plurality of locations in the external memory using the read key, reading data from the plurality of locations in the external memory in accordance with the sparse set of reading weights, generating a set of writing weights that includes a respective writing weight for each of the plurality of locations in the external memory, and writing the write vector to the plurality of locations in the external memory in accordance with the writing weights.