# X2-Softmax: Margin Adaptive Loss Function for Face Recognition

arXiv: https://arxiv.org/abs/2312.05281 · HTML: https://mlsanity.com/paper/2312.05281/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 8 Dec 2023.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [VGGFace2: A dataset for recognising faces across pose and age](https://mlsanity.com/paper/1710.08092/) (2017)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [MS-Celeb-1M: A Dataset and Benchmark for Large-Scale Face Recognition](https://mlsanity.com/paper/1607.08221/) (2016)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Deep metric learning using Triplet network](https://mlsanity.com/paper/1412.6622/) (2014)
- [Multi-Similarity Loss with General Pair Weighting for Deep Metric Learning](https://mlsanity.com/paper/1904.06627/) (2019)
- [MagFace: A Universal Representation for Face Recognition and Quality Assessment](https://mlsanity.com/paper/2103.06627/) (2021)
- [Large-Margin Softmax Loss for Convolutional Neural Networks](https://mlsanity.com/paper/1612.02295/) (2016)
- [Additive Margin Softmax for Face Verification](https://mlsanity.com/paper/1801.05599/) (2018)
- [Cross-Age LFW: A Database for Studying Cross-Age Face Recognition in Unconstrained Environments](https://mlsanity.com/paper/1708.08197/) (2017)
- [NormFace: L2 Hypersphere Embedding for Face Verification](https://mlsanity.com/paper/1704.06369/) (2017)
- [RetinaFace: Single-stage Dense Face Localisation in the Wild](https://mlsanity.com/paper/1905.00641/) (2019)
- [ElasticFace: Elastic Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/2109.09416/) (2021)
- [Triplet-Center Loss for Multi-View 3D Object Retrieval](https://mlsanity.com/paper/1803.06189/) (2018)
- [SimpleX: A Simple and Strong Baseline for Collaborative Filtering](https://mlsanity.com/paper/2109.12613/) (2021)
- [Masked Face Recognition Challenge: The InsightFace Track Report](https://mlsanity.com/paper/2108.08191/) (2021)
- [GroupFace: Learning Latent Groups and Constructing Group-based Representations for Face Recognition](https://mlsanity.com/paper/2005.10497/) (2020)
- [Towards Universal Backward-Compatible Representation Learning](https://mlsanity.com/paper/2203.01583/) (2022)
- [Generating Photo-Realistic Training Data to Improve Face Recognition Accuracy](https://mlsanity.com/paper/1811.00112/) (2018)
- [Support Vector Guided Softmax Loss for Face Recognition](https://mlsanity.com/paper/1812.11317/) (2018)
- [Deep Rival Penalized Competitive Learning for Low-resolution Face Recognition](https://mlsanity.com/paper/2108.01286/) (2021)

## Built on by (most cited first, 3 of 3)

- [GroupFace: Imbalanced Age Estimation Based on Multi-hop Attention Graph Convolutional Network and Group-aware Margin Optimization](https://mlsanity.com/paper/2412.11450/) (2024)
- [EPL: Empirical Prototype Learning for Deep Face Recognition](https://mlsanity.com/paper/2405.12447/) (2024)
- [AdaSin: Enhancing Hard Sample Metrics with Dual Adaptive Penalty for Face Recognition](https://mlsanity.com/paper/2503.03528/) (2025)

## Abstract (arXiv)

Learning the discriminative features of different faces is an important task in face recognition. By extracting face features in neural networks, it becomes easy to measure the similarity of different face images, which makes face recognition possible. To enhance the neural network's face feature separability, incorporating an angular margin during training is common practice. State-of-the-art loss functions CosFace and ArcFace apply fixed margins between weights of classes to enhance the inter-class separation of face features. Since the distribution of samples in the training set is imbalanced, similarities between different identities are unequal. Therefore, using an inappropriately fixed angular margin may lead to the problem that the model is difficult to converge or the face features are not discriminative enough. It is more in line with our intuition that the margins are angular adaptive, which could increase with the angles between classes growing. In this paper, we propose a new angular margin loss named X2-Softmax. X2-Softmax loss has adaptive angular margins, which provide the margin that increases with the angle between different classes growing. The angular adaptive margin ensures model flexibility and effectively improves the effect of face recognition. We have trained the neural network with X2-Softmax loss on the MS1Mv3 dataset and tested it on several evaluation benchmarks to demonstrate the effectiveness and superiority of our loss function.