The j-th taskspecific language adversarial network estimates language labels from the j-th task-specific hidden representations.
the cross-entropy loss functions of each network are defined as: where L o , L x , and L y are the cross entropy loss terms for the classification networks, the task adversarial networks, and the language adversarial networks.ô n,i are the reference probabilities, and o n,k , x n,j , and y n,i are the estimated probabilities of the k-th label in the j-th task classification network, the j -th task in the ith language-specific task adversarial network, and  the i -th language in the j-th task-specific language adversarial network for W n , respectively.