A device configured to implement an artificial intelligence deep neural network includes a first matrix and a second matrix. The first matrix resistive processing unit (“RPU”) array receives a first input vector along the rows of the first matrix RPU. A second matrix RPU array receives a second input vector along the rows of the second matrix RPU. A reference matrix RPU array receives an inverse of the first input vector along the rows of the reference matrix RPU and an inverse of the second input vector along the rows of the reference matrix RPU. A plurality of analog to digital converters are coupled to respective outputs of a plurality of summing junctions that receive respective column outputs of the first matrix RPU array, the second matrix RPU array, and the reference RPU array and provides a digital value of the output of the plurality of summing junctions.