# ExpFace: Exponential Angular Margin Loss for Deep Face Recognition

arXiv: https://arxiv.org/abs/2509.19753 · HTML: https://mlsanity.com/paper/2509.19753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Circle Loss: A Unified Perspective of Pair Similarity Optimization](https://mlsanity.com/paper/2002.10857/) (2020)
- [AdaFace: Quality Adaptive Margin for Face Recognition](https://mlsanity.com/paper/2204.00964/) (2022)
- [MagFace: A Universal Representation for Face Recognition and Quality Assessment](https://mlsanity.com/paper/2103.06627/) (2021)
- [CurricularFace: Adaptive Curriculum Learning Loss for Deep Face Recognition](https://mlsanity.com/paper/2004.00288/) (2020)
- [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)
- [WebFace260M: A Benchmark Unveiling the Power of Million-Scale Deep Face Recognition](https://mlsanity.com/paper/2103.04098/) (2021)
- [The MegaFace Benchmark: 1 Million Faces for Recognition at Scale](https://mlsanity.com/paper/1512.00596/) (2015)
- [Deep Pyramidal Residual Networks](https://mlsanity.com/paper/1610.02915/) (2016)
- [ElasticFace: Elastic Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/2109.09416/) (2021)
- [AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations](https://mlsanity.com/paper/1905.00292/) (2019)
- [Killing Two Birds with One Stone:Efficient and Robust Training of Face Recognition CNNs by Partial FC](https://mlsanity.com/paper/2203.15565/) (2022)
- [Mis-classified Vector Guided Softmax Loss for Face Recognition](https://mlsanity.com/paper/1912.00833/) (2019)
- [SphereFace Revived: Unifying Hyperspherical Face Recognition](https://mlsanity.com/paper/2109.05565/) (2021)

## Built on by (most cited first, 1 of 1)

- [Towards Robust Classroom Attendance: A Comprehensive Evaluation of Face Detection and Recognition Models](https://mlsanity.com/paper/2609.22750/) (2026)

## Abstract (arXiv)

Face recognition is an open-set problem requiring high discriminative power to ensure that intra-class distances remain smaller than inter-class distances. Margin-based softmax losses, such as SphereFace, CosFace, and ArcFace, have been widely adopted to enhance intra-class compactness and inter-class separability, yet they overlook the impact of noisy samples. By examining the distribution of samples in the angular space, we observe that clean samples predominantly cluster in the center region, whereas noisy samples tend to shift toward the peripheral region. Motivated by this observation, we propose the Exponential Angular Margin Loss (ExpFace), which introduces an angular exponential term as the margin. This design applies a larger penalty in the center region and a smaller penalty in the peripheral region within the angular space, thereby emphasizing clean samples while suppressing noisy samples. We present a unified analysis of ExpFace and classical margin-based softmax losses in terms of margin embedding forms, similarity curves, and gradient curves, showing that ExpFace not only avoids the training instability of SphereFace and the non-monotonicity of ArcFace, but also exhibits a similarity curve that applies penalties in the same manner as the decision boundary in the angular space. Extensive experiments demonstrate that ExpFace achieves state-of-the-art performance. To facilitate future research, we have released the source code at: https://github.com/dfr-code/ExpFace.