Bhavin_Jawade:

Without early stopping ArcFace loss network overfits on training classification data and gives very poor performance on validation verification task.


This seems to give the answer. 
Based on this statement it seems that you can (somehow) quantify that the model is overfitting and gives poor performance on the validation set. Assuming you can measure this overfitting as well as the performance on the training and validation set, you could use this metric also for early stopping.