L2-constrained Softmax Loss for Discriminative Face Verification

By Rajeev Ranjan, Carlos Domingo Castillo, Ramalingam Chellappa. arXiv.org, 2017

482 citations recorded by the source corpus.

In recent years, the performance of face verification systems has significantly improved using deep convolutional neural networks (DCNNs). A typical pipeline for face verification includes training a deep network for subject classification with softmax loss, using the penultimate layer output as the feature descriptor, and generating a cosine similarity score given a pair of face images. The softmax loss function does not optimize the features to have higher similarity score for positive pairs and lower similarity score for negative pairs, which leads to a performance gap. In this paper, we add an L2-constraint to the feature descriptors which restricts them to lie on a hypersphere of a fixed radius. This module can be easily implemented using existing deep learning frameworks. We show that integrating this simple step in the training pipeline significantly boosts the performance of face verification. Specifically, we achieve state-of-the-art results on the challenging IJB-A dataset, achieving True Accept Rate of 0.909 at False Accept Rate 0.0001 on the face verification protocol. Additionally, we achieve state-of-the-art performance on LFW dataset with an accuracy of 99.78%, and competing performance on YTF dataset with accuracy of 96.08%.

Subfields: Computer Vision and Pattern Recognition, Neurology, Signal Processing

View Paper: https://www.semanticscholar.org/paper/57a807f65e61bbba0ea3ba02572cc5843ecef2b6

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Citations in the corpus

A Comprehensive Study on Center Loss for Deep Face Recognition (2019, background): “– Compared to the softmax loss family Recently, (Wang et al. 2017; Ranjan et al. 2017; Liu et al. 2017a) reformulate the softmax loss as metric learning approaches for face recognition.”
Decoupled Networks (2018, background): “[23, 17, 24] normalize the input features before entering the last fully connected layer, achieving promising performance on face recognition.”
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].”
Are we really making much progress?: Revisiting, benchmarking and refining heterogeneous graph neural networks (2021, background): “Additionally, it suggests to multiply a scaling parameter α to the output embedding [26].”
Semi-Supervised Domain Adaptation via Minimax Entropy (2019, methodology): “We introduce an ablation study on the classifier network architecture proposed in [5, 25] with AlexNet on DomainNet.”
Heated-Up Softmax Embedding (2018, background): “A similar conclusion is also reported by Ranjan et al. (2017).”
DarkRank: Accelerating Deep Metric Learning via Cross Sample Similarities Transfer (2017, background): “While constraining the embedding to live on the unit hypersphere is a standard setting for metric learning methods in person re-identification filed, a recent work[40] shows that small α can hurt the representing ability of embeddings, and suggests to make α a tunable parameter.”
Past, Present, and Future of Face Recognition: A Review (2020, methodology): “Several promising ideas have been explored to bring advances in CNNs, such as the use of proper activation [143] and various loss functions [15,124–126,130,134,136,138,141,142,145,148–152], the use of metric learning algorithms [38,127], normalization of features and weights [133,135,139], extractio”
Circle Loss: A Unified Perspective of Pair Similarity Optimization (2020, background): “Re-scaling the cosine similarity under supervision is a common practice in modern classification losses [21, 30, 29, 32, 39, 40].”
Data Uncertainty Learning in Face Recognition (2020, methodology): “∑C c e wcsi , (3) In practice, we use different variants of Lsoftmax such as additive margin [40], feature l2 normalization [32] and arcface [7], to train our face classification model.”
NormFace: L2 Hypersphere Embedding for Face Verification (2017, methodology): “L2-softmax[24] shares a similar analysis about the convergence problem described in Section 3.”
AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations (2019, methodology): “in [28] also discussed this problem and applied normalization on learned feature vectors to restrict them lying on a hypersphere.”
Improving Network Robustness against Adversarial Attacks with Compact Convolution (2017, methodology): “To enforce centrality and compactness constraints to the network features, we explore different loss functions such as CenterLoss [28] and L 2 -Softmax Loss [22].”
Additive Margin Softmax for Face Verification (2018, methodology): “[6, 12, 15] also improved the softmax loss by incorporating differnet kinds of margins.”
Sampled Softmax with Random Fourier Features (2019, background): “We note that normalized embeddings are widely used in practice to improve training stability and model quality [28, 29, 30].”
Angular Visual Hardness (2019, background): “, 2017c) and face recognition (Wang et al., 2017; Ranjan et al., 2017), indicating that AVH is generally effective to improve generalization in various tasks.”
Deep Face Recognition: A Survey (2018, result): “[157], [206], [74], [130] [155], [25], [75]”
Boosting Adversarial Training with Hypersphere Embedding (2020, methodology): “The implementation of HE mainly consists of three typical operations including feature normalization (FN) (Ranjan et al., 2017), weight normalization (WN) (Guo & Zhang, 2017), and angular margins (AM) (Liu et al., 2016), i.e., HE=FN+WN+AM, as detailed below.”