Despite significant progress made over the past twenty five years, unconstrained face verification remains a challenging problem. This paper proposes an approach that couples a deep CNN-based approach with a low-dimensional discriminative embedding learned using triplet probability constraints to solve the unconstrained face verification problem. Aside from yielding performance improvements, this embedding provides significant advantages in terms of memory and for post-processing operations like subject specific clustering. Experiments on the challenging IJB-A dataset show that the proposed algorithm performs comparably or better than the state of the art methods in verification and identification metrics, while requiring much less training data and training time. The superior performance of the proposed method on the CFP dataset shows that the representation learned by our deep CNN is robust to extreme pose variation. Furthermore, we demonstrate the robustness of the deep features to challenges including age, pose, blur and clutter by performing simple clustering experiments on both IJB-A and LFW datasets.