A memristive device is described. The memristive device includes a first layer having a first plurality of conductive lines, a second layer having a second plurality of conductive lines, and memristive interlayer connectors. The first and second layers differ. The first and second pluralities of conductive lines are each lithographically defined. The first and second pluralities of conductive lines are insulated from each other. The memristive interlayer connectors are memristively coupled with a first portion of the first plurality of conductive lines and memristively coupled with a second portion of the second plurality of conductive lines. The memristive interlayer connectors are thus sparsely coupled with the first and second pluralities of conductive lines. Each memristive interlayer connector includes a conductive portion and a memristive portion. The memristive portion is between the conductive portion and corresponding line(s) of the first plurality of conductive lines and/or the second plurality of conductive lines.