NormFace: L2 Hypersphere Embedding for Face Verification

By Feng Wang, Xiang Xiang, Jian Cheng, Alan L. Yuille. 2017

801 citations recorded by the source corpus.

Thanks to the recent developments of Convolutional Neural Networks, the performance of face verification methods has increased rapidly. In a typical face verification method, feature normalization is a critical step for boosting performance. This motivates us to introduce and study the effect of normalization during training. But we find this is non-trivial, despite normalization being differentiable. We identify and study four issues related to normalization through mathematical analysis, which yields understanding and helps with parameter settings. Based on this analysis we propose two strategies for training using normalized features. The first is a modification of softmax loss, which optimizes cosine similarity instead of inner-product. The second is a reformulation of metric learning by introducing an agent vector for each class. We show that both strategies, and small variants, consistently improve performance by between 0.2% to 0.4% on the LFW dataset based on two models. This is significant because the performance of the two models on LFW dataset is close to saturation at over 98%.

Subfields: Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning

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Citations in the corpus

Maintaining Discrimination and Fairness in Class Incremental Learning (2019, methodology): “It is interesting to see the effect of adding a normalization layer on the weights (in the FC layer) directly, like the operation in Modiﬁed Softmax Loss [21] and NormFace [30], so that the weights of all classes can have a unit norm.”
Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere (2020, background): “Existing works have motivated this choice from a manifold mapping perspective (Liu et al., 2017; Davidson et al., 2018) and computation stability (Xu & Durrett, 2018; Wang et al., 2017).”
CosFace: Large Margin Cosine Loss for Deep Face Recognition (2018, background): “[38] normalizes the weights which replace the inner product with cosine”
Low-Shot Learning with Imprinted Weights (2017, methodology): “Inspired by the use of embeddings as proxies [11] or agents [24] for individual object classes, we argue that embedding vectors can be effectively compared to weights in the last linear layer of ConvNet classifiers.”
Clustering-Oriented Representation Learning with Attractive-Repulsive Loss (2018, methodology): “…for the domain of image classiﬁcation, where the problem of needing discriminative features is only understood as necessary for image problems, particularly facial recognition (Wang et al. 2017; Ranjan, Castillo, and Chellappa 2017; Gao et al. 2018; Wang et al. 2018; Zheng, Pal, and Savvides 2018).”
Why Do Better Loss Functions Lead to Less Transferable Features? (2020, background): “Similar losses have appeared in previous literature [54, 71, 76, 72, 73, 21, 38, 15], and variants have introduced explicit additive or multiplicative margins to this loss that we do not consider here [38, 72, 73, 21].”
Feature Normalized Knowledge Distillation for Image Classification (2020, methodology): “Wang et al. [35] has proven that a feature f with bigger L 2 -norm could produce a harder distribution and ﬁt one-hot label better.”
Sampled Softmax with Random Fourier Features (2019, background): “[30] Feng Wang, Xiang Xiang, Jian Cheng, and Alan Loddon Yuille.”
Heated-Up Softmax Embedding (2018, methodology): “In face veriﬁcation, training a classiﬁer and using the output of the bottleneck layer as embedding performs reasonably well (Wang et al., 2017b).”
Improving Lexical Choice in Neural Machine Translation (2017, background): “This coincides with other observations that NMT’s translations are often ﬂuent but lack accuracy (Wang et al., 2017; Wu et al., 2016).”
Dissecting Supervised Constrastive Learning (2021, background): “This is in line with the special case of equinorm representations and weights, presented in (Wang et al., 2017), and complements a recent optimality result by Papyan et al. (2020) (cf. Remark 2 for details).”
SphereFace Revived: Unifying Hyperspherical Face Recognition (2021, methodology): “Another significant difference between SphereFace and other hyperspherical FR methods [3], [4], [5], [9] is whether feature normalization (FN) is performed.”
Learning with Imprinted Weights (2017, methodology): “Inspired by the use of embeddings as proxies [10] or agents [24] for individual object classes, we argue that embedding vectors can be effectively compared to weights in the last linear layer of ConvNet classifiers.”
Visual Attention Methods in Deep Learning: An In-Depth Survey (2022, methodology): “Firstly, they compute image-text cross attention by a few steps as follows: a) compute cosine similarity for all image-text pairs [144] followed by l2 normalization [145], b) compute the weighted sum of these pairs attentions, where the image one is calculated by softmax [146], c) the final similari”
AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations (2019, methodology): “The cosine-based softmax losses [21, 28, 39, 8] and their variants [40, 38, 7] achieve great success in deep learning based face recognition.”
Past, Present, and Future of Face Recognition: A Review (2020, methodology): “use of metric learning algorithms [127, 38], normalization of features and weights [135, 133, 139],”