The standard loss function used to train neural network classifiers, categorical cross-entropy (CCE), seeks to maximize accuracy on the training data; building useful representations is not a necessary byproduct of this objective. In this work, we propose clustering-oriented representation learning (COREL) as an alternative to CCE in the context of a generalized attractive-repulsive loss framework. COREL has the consequence of building latent representations that collectively exhibit the quality of natural clustering within the latent space of the final hidden layer, according to a predefined similarity function. Despite being simple to implement, COREL variants outperform or perform equivalently to CCE in a variety of scenarios, including image and news article classification using both feed-forward and convolutional neural networks. Analysis of the latent spaces created with different similarity functions facilitates insights on the different use cases COREL variants can satisfy, where the Cosine-COREL variant makes a consistently clusterable latent space, while Gaussian-COREL consistently obtains better classification accuracy than CCE.
Recently there have been many approaches using either cosine- or Gaussian-based loss functions. Most of these are used explicitly for the domain of image classification, where the problem of needing discriminative features is only understood as necessary for image problems, particularly facial recognition @cite_19 @cite_2 @cite_21 @cite_12 @cite_7 . Some recent work has combined cosine similarity with weight imprinting @cite_24 , which sets @math for @math to be dynamically computed latent centroids (as in center loss @cite_1 ); they then apply the softmax operation over the cosine similarities, as in congenerous cosine loss @cite_29 . Other work models image classes as Gaussians @cite_16 , but requires learning the covariance matrix @math in the similarity function, which is constrained to be diagonal.
@cite_7 @cite_29 @cite_21 @cite_1 @cite_24 @cite_19 @cite_2 @cite_16 @cite_12
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Face recognition has achieved revolutionary advancement owing to the advancement of the deep convolutional neural network (CNN). The central task of face recognition, including face verification and identification, involves face feature discrimination. However, traditional softmax loss of deep CNN usually lacks the power of discrimination. To address this problem, recently several loss functions such as central loss centerloss , large margin softmax loss lsoftmax , and angular softmax loss sphereface have been proposed. All these improvement algorithms share the same idea: maximizing inter-class variance and minimizing intra-class variance. In this paper, we design a novel loss function, namely large margin cosine loss (LMCL), to realize this idea from a different perspective. More specifically, we reformulate the softmax loss as cosine loss by L2 normalizing both features and weight vectors to remove radial variation, based on which a cosine margin term is introduced to further maximize decision margin in angular space. As a result, minimum intra-class variance and maximum inter-class variance are achieved by normalization and cosine decision margin maximization. We refer to our model trained with LMCL as CosFace. To test our approach, extensive experimental evaluations are conducted on the most popular public-domain face recognition datasets such as MegaFace Challenge, Youtube Faces (YTF) and Labeled Face in the Wild (LFW). We achieve the state-of-the-art performance on these benchmark experiments, which confirms the effectiveness of our approach. Face recognition has made extraordinary progress owing to the advancement of deep convolutional neural networks (CNNs). The central task of face recognition, including face verification and identification, involves face feature discrimination. However, the traditional softmax loss of deep CNNs usually lacks the power of discrimination. To address this problem, recently several loss functions such as center loss, large margin softmax loss, and angular softmax loss have been proposed. All these improved losses share the same idea: maximizing inter-class variance and minimizing intra-class variance. In this paper, we propose a novel loss function, namely large margin cosine loss (LMCL), to realize this idea from a different perspective. More specifically, we reformulate the softmax loss as a cosine loss by L2 normalizing both features and weight vectors to remove radial variations, based on which a cosine margin term is introduced to further maximize the decision margin in the angular space. As a result, minimum intra-class variance and maximum inter-class variance are achieved by virtue of normalization and cosine decision margin maximization. We refer to our model trained with LMCL as CosFace. Extensive experimental evaluations are conducted on the most popular public-domain face recognition datasets such as MegaFace Challenge, Youtube Faces (YTF) and Labeled Face in the Wild (LFW). We achieve the state-of-the-art performance on these benchmarks, which confirms the effectiveness of our proposed approach. Feature matters. How to train a deep network to acquire discriminative features across categories and polymerized features within classes has always been at the core of many computer vision tasks, specially for large-scale recognition systems where test identities are unseen during training and the number of classes could be at million scale. In this paper, we address this problem based on the simple intuition that the cosine distance of features in high-dimensional space should be close enough within one class and far away across categories. To this end, we proposed the congenerous cosine (COCO) algorithm to simultaneously optimize the cosine similarity among data. It inherits the softmax property to make inter-class features discriminative as well as shares the idea of class centroid in metric learning. Unlike previous work where the center is a temporal, statistical variable within one mini-batch during training, the formulated centroid is responsible for clustering inner-class features to enforce them polymerized around the network truncus. COCO is bundled with discriminative training and learned end-to-end with stable convergence. Experiments on five benchmarks have been extensively conducted to verify the effectiveness of our approach on both small-scale classification task and large-scale human recognition problem. One of the main challenges in feature learning using Deep Convolutional Neural Networks (DCNNs) for large-scale face recognition is the design of appropriate loss functions that enhance discriminative power. Centre loss penalises the distance between the deep features and their corresponding class centres in the Euclidean space to achieve intra-class compactness. SphereFace assumes that the linear transformation matrix in the last fully connected layer can be used as a representation of the class centres in an angular space and penalises the angles between the deep features and their corresponding weights in a multiplicative way. Recently, a popular line of research is to incorporate margins in well-established loss functions in order to maximise face class separability. In this paper, we propose an Additive Angular Margin Loss (ArcFace) to obtain highly discriminative features for face recognition. The proposed ArcFace has a clear geometric interpretation due to the exact correspondence to the geodesic distance on the hypersphere. We present arguably the most extensive experimental evaluation of all the recent state-of-the-art face recognition methods on over 10 face recognition benchmarks including a new large-scale image database with trillion level of pairs and a large-scale video dataset. We show that ArcFace consistently outperforms the state-of-the-art and can be easily implemented with negligible computational overhead. We release all refined training data, training codes, pre-trained models and training logs, which will help reproduce the results in this paper.