Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for processing and storing inputs for use in a neural network. One of the methods includes receiving input data for storage in a memory system comprising a first set of memory blocks, the memory blocks having an associated order; passing the input data to a highest ordered memory block; for each memory block for which there is a lower ordered memory block: applying a filter function to data currently stored by the memory block to generate filtered data and passing the filtered data to a lower ordered memory block; and for each memory block: combining the data currently stored in the memory block with the data passed to the memory block to generate updated data, and storing the updated data in the memory block.