Cross$-$entropy is used for multi$-$category classification loss. If the output of softmax is given by A and the ground truth is given by $Y=[y^{(1)},y^{(2)},$dots,$y^{(m)}],$

the cross entropy loss between the predictions A and groundtruth labels $Y$ is given by$,$ Loss$(A,Y)=-\frac{1}{m}{\displaystyle \underset{i=1}{\overset{m}{}}}{\displaystyle \underset{k=1}{\overset{n}{}}}I\{y^i=k\}log{a}_k^i$

where I is the identity function given by $,$I condition