The document proposes an additive margin softmax loss function to improve on the standard softmax loss for deep face recognition. It aims to minimize intra-class variation by adding a regularization term to penalize feature-to-center distances and using a scale parameter, which produces higher gradients to further shrink variance within classes. This approach incorporates a fixed hard angular margin, unlike angular softmax which only imposes an unfixed margin, helping to push classification boundaries closer to each class's weight vector.