A system for compressed data storage using a neural network. The system comprises a memory comprising a plurality of memory locations configured to store data; a query neural network configured to process a representation of an input data item to generate a query; an immutable key data store comprising key data for indexing the plurality of memory locations; an addressing system configured to process the key data and the query to generate a weighting associated with the plurality of memory locations; a memory read system configured to generate output memory data from the memory based upon the generated weighting associated with the plurality of memory locations and the data stored at the plurality of memory locations; and a memory write system configured to write received write data to the memory based upon the generated weighting associated with the plurality of memory locations.