This paper proposes a novel and interpretable objective function called Additive Margin Softmax (AM-Softmax) for deep face verification. The goal is to learn face features that have small intra-class variation and large inter-class differences, which is crucial for achieving good performance in face verification tasks. Unlike previous methods that use multiplicative angular margins, AM-Softmax introduces an additive angular margin, which is more intuitive and interpretable. The paper also emphasizes the importance of feature normalization in achieving better performance. The AM-Softmax loss function is formulated as $ \psi(\theta) = \cos\theta - m $, where $ m $ is a margin parameter. This formulation is simpler than previous methods and leads to better performance. The loss function is implemented with feature and weight normalization, and a global scale factor $ s $ is used to scale the cosine values. The loss function is shown to perform better than existing state-of-the-art methods on benchmark datasets such as LFW and MegaFace. The paper also discusses the geometric interpretation of the AM-Softmax loss function, showing how it affects the decision boundary in the hypersphere manifold. It compares the angular margin and cosine margin approaches, noting that while angular margin is conceptually better, cosine margin is more computationally efficient. The paper also highlights the importance of feature normalization, especially for low-quality images, and shows that feature normalization leads to better performance. Experiments on various datasets show that the AM-Softmax loss function outperforms existing methods in terms of performance and convergence. The paper also discusses the effect of hyper-parameters such as $ m $ and $ s $, showing that the performance of the loss function is sensitive to these parameters. The paper concludes that AM-Softmax is a simple and effective method for deep face verification, and that further research is needed to explore other ways of specifying the function $ \psi(\theta) $.This paper proposes a novel and interpretable objective function called Additive Margin Softmax (AM-Softmax) for deep face verification. The goal is to learn face features that have small intra-class variation and large inter-class differences, which is crucial for achieving good performance in face verification tasks. Unlike previous methods that use multiplicative angular margins, AM-Softmax introduces an additive angular margin, which is more intuitive and interpretable. The paper also emphasizes the importance of feature normalization in achieving better performance. The AM-Softmax loss function is formulated as $ \psi(\theta) = \cos\theta - m $, where $ m $ is a margin parameter. This formulation is simpler than previous methods and leads to better performance. The loss function is implemented with feature and weight normalization, and a global scale factor $ s $ is used to scale the cosine values. The loss function is shown to perform better than existing state-of-the-art methods on benchmark datasets such as LFW and MegaFace. The paper also discusses the geometric interpretation of the AM-Softmax loss function, showing how it affects the decision boundary in the hypersphere manifold. It compares the angular margin and cosine margin approaches, noting that while angular margin is conceptually better, cosine margin is more computationally efficient. The paper also highlights the importance of feature normalization, especially for low-quality images, and shows that feature normalization leads to better performance. Experiments on various datasets show that the AM-Softmax loss function outperforms existing methods in terms of performance and convergence. The paper also discusses the effect of hyper-parameters such as $ m $ and $ s $, showing that the performance of the loss function is sensitive to these parameters. The paper concludes that AM-Softmax is a simple and effective method for deep face verification, and that further research is needed to explore other ways of specifying the function $ \psi(\theta) $.