Title: Feature Incay for Representation Regularization. Abstract: Softmax-based loss is widely used in deep learning for multi-class classification, where each class is represented by a weight vector and each sample is represented as a feature vector. Different from traditional learning algorithms where features are pre-defined and only weight vectors are tunable through training, feature vectors are also tunable as representation learning in deep learning. Thus we investigate how to improve the classification performance by better adjusting the features. One main observation is that elongating the feature norm of both correctly-classified and mis-classified feature vectors improves learning: (1) increasing the feature norm of correctly-classified examples induce smaller training loss; (2) increasing the feature norm of mis-classified examples can upweight the contribution from hard examples. Accordingly, we propose feature incay to regularize representation learning by encouraging larger feature norm. In contrast to weight decay which shrinks the weight norm, feature incay is proposed to stretch the feature norm. Extensive empirical results on MNIST, CIFAR10, CIFAR100 and LFW demonstrate the effectiveness of feature incay. 