ND4J: “N-Dimensional Arrays for Java”. ND4J is the mathematical backend upon which DL4J is built. All of DL4J’s neural networks are built using the operations (matrix multiplications, vector operations, etc) in ND4J. ND4J is how DL4J supports both CPU and GPU training of networks, without any changes to the networks themselves. Without ND4J, there would be no DL4J.