We present a novel framework to exploit privileged information for recognition which is provided only during the training phase. Here, we focus on recognition task where images are provided as the main view and soft biometric traits (attributes) are provided as the privileged data (only available during training phase). We demonstrate that more discriminative feature space can be learned by enforcing a deep network to adjust adaptive margins between classes utilizing attributes. This tight constraint also effectively reduces the class imbalance inherent in the local data neighborhood, thus carving more balanced class boundaries locally and using feature space more efficiently. Extensive experiments are performed on five different datasets and the results show the superiority of our method compared to the state-of-the-art models in both tasks of face recognition and person re-identification.