The paper introduces ArcFace, a loss function that "not only has a clear geometric interpretation but also significantly enhances the discriminative power." Beyond this core contribution, the authors propose sub-center ArcFace to address noisy training data by allowing samples to match multiple sub-centers within each identity class. The work also explores model inversion, demonstrating that pre-trained ArcFace networks can generate identity-preserving face images using network gradients and batch normalization statistics, without requiring additional generators or discriminators.

Face recognition via deep convolutional neural networks involves mapping normalized face images into discriminative feature embeddings where "small intra-class and large inter-class distance" characterizes quality representations. The field traditionally follows two main approaches: softmax-based multi-class classifiers and embedding-based methods like triplet loss.

The softmax loss suffers from two key drawbacks: learned features may be "separable for the closed-set classification problem but not discriminative enough for the open-set face recognition problem," and the weight matrix size "increases linearly with the identities number." Triplet loss presents challenges through "combinatorial explosion in the number of face triplets" and difficult semi-hard sample mining.

Rather than sample-to-sample comparisons, ArcFace conducts "global sample-to-class and sample-to-subclass comparisons with angular margins." The method normalizes features and centers, then applies an "additive angular margin to the target angle," leveraging the "exact correspondence between the angle and arc in the normalized hypersphere."

Pioneering work using triplet loss "exploits triplet data such that faces from the same class are closer than faces from different classes by a clear Euclidean distance margin." However, sample comparisons remain "local within mini-batch" and "combinatorial explosion" requires careful triplet mining strategies.

Recent margin-based softmax methods incorporating margin penalties conduct "global comparisons at the cost of memory consumption on holding the center of each class." Most face datasets are "downloaded from the Internet by searching a pre-defined celebrity list" with "ambiguous and inaccurate" original labels. While GAN-based approaches can "yield high-fidelity images," they require original training data access.

Starting from standard softmax loss, the authors normalize both weights and features, transforming the logit relationship into "cos θⱼ where θⱼ is the angle between the weight and the feature." This normalization ensures "predictions only depend on the angle between the feature and the weight," distributing learned embeddings "on a hypersphere with a radius of s."

The method introduces a margin penalty m to "simultaneously enhance the intra-class compactness and inter-class discrepancy." Unlike multiplicative margins that produce "nonlinear angular margins," ArcFace maintains "a constant linear angular margin throughout the whole interval," providing clearer geometric interpretation through precise geodesic distance correspondence on normalized hyperspheres.

Standard ArcFace assumes clean training data but "training data are not clean especially when the dataset is in large scale." Instead of enforcing all samples close to a single center, the method assigns K sub-centers per identity. Samples need only "be close to any of the K positive sub-centers instead of the only one positive center."

This relaxation allows hard samples and noisy instances to "form a non-dominant sub-class" separately from clean majority samples. The noise rate in dominant sub-classes "decreases from 38.47% to 12.40%," reducing apparent noise to approximately one-third.

The authors explore the inverse problem: "mapping from a low-dimensional latent space to a highly nonlinear face space." Given a pre-trained model, random input tensors undergo gradient-based optimization toward pre-defined identity targets. Face generation employs "statistic priors stored in the BN layers" as constraints. Unlike DeepDream's total-variation regularization producing "not realistic" results or GAN-based synthesis requiring original data access, this gradient-based approach leverages learned statistical distributions within the model itself.

Experiments employ multiple datasets including CASIA (0.5M images, 10K identities), VGG2 (3.3M images), MS1MV0 (10M raw images with ~50% noise), and MS1MV3 (5.1M cleaned images). Testing on LFW achieves 99.83%, on YTF 98.01%. On IJB-C at TPR@FPR=1e-4, the method reaches 97.27% verification accuracy. Sub-center ArcFace with K=3 sub-centers achieves 93.72% on IJB-C, while standard ArcFace drops to 90.27% with noisy data. After automatic cleaning, performance improves to 95.92%.

ArcFace provides an intuitive, efficient margin-based softmax loss with "clear geometric interpretation" through angular margin formulation on normalized hyperspheres. Sub-center ArcFace extends the approach to handle massive real-world noise. Pre-trained ArcFace models can function as generative models, reconstructing identity-preserved faces through gradient-based optimization constrained by batch normalization statistics.