# Sparsity-Inducing Divergence Losses for Biometric Verification

arXiv: https://arxiv.org/abs/2606.31664 · HTML: https://mlsanity.com/paper/2606.31664/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (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)
- [VoxCeleb2: Deep Speaker Recognition](https://mlsanity.com/paper/1806.05622/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [AdaFace: Quality Adaptive Margin for Face Recognition](https://mlsanity.com/paper/2204.00964/) (2022)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [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)
- [Cross-Age LFW: A Database for Studying Cross-Age Face Recognition in Unconstrained Environments](https://mlsanity.com/paper/1708.08197/) (2017)
- [MobileFaceNets: Efficient CNNs for Accurate Real-Time Face Verification on Mobile Devices](https://mlsanity.com/paper/1804.07573/) (2018)
- [Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints](https://mlsanity.com/paper/2309.16240/) (2023)
- [Sparse Sequence-to-Sequence Models](https://mlsanity.com/paper/1905.05702/) (2019)
- [Partial FC: Training 10 Million Identities on a Single Machine](https://mlsanity.com/paper/2010.05222/) (2020)
- [ElasticFace: Elastic Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/2109.09416/) (2021)
- [R'enyi Divergence Variational Inference](https://mlsanity.com/paper/1602.02311/) (2016)
- [Killing Two Birds with One Stone:Efficient and Robust Training of Face Recognition CNNs by Partial FC](https://mlsanity.com/paper/2203.15565/) (2022)
- [WebFace260M: A Benchmark for Million-Scale Deep Face Recognition](https://mlsanity.com/paper/2204.10149/) (2022)
- [Learning Classifiers with Fenchel-Young Losses: Generalized Entropies, Margins, and Algorithms](https://mlsanity.com/paper/1805.09717/) (2018)
- [Margin Matters: Towards More Discriminative Deep Neural Network Embeddings for Speaker Recognition](https://mlsanity.com/paper/1906.07317/) (2019)
- [The IDLAB VoxSRC-20 Submission: Large Margin Fine-Tuning and Quality-Aware Score Calibration in DNN Based Speaker Verification](https://mlsanity.com/paper/2010.11255/) (2020)
- [Cluster and Aggregate: Face Recognition with Large Probe Set](https://mlsanity.com/paper/2210.10864/) (2022)
- [A Quality Aware Sample-to-Sample Comparison for Face Recognition](https://mlsanity.com/paper/2306.04000/) (2023)
- [TopoFR: A Closer Look at Topology Alignment on Face Recognition](https://mlsanity.com/paper/2410.10587/) (2024)
- [An Efficient Training Approach for Very Large Scale Face Recognition](https://mlsanity.com/paper/2105.10375/) (2021)
- [KappaFace: Adaptive Additive Angular Margin Loss for Deep Face Recognition](https://mlsanity.com/paper/2201.07394/) (2022)
- [Loss Functions and Operators Generated by f-Divergences](https://mlsanity.com/paper/2501.18537/) (2025)
- [The VoxCeleb Speaker Recognition Challenge: A Retrospective](https://mlsanity.com/paper/2408.14886/) (2024)
- [f-Divergence Based Classification: Beyond the Use of Cross-Entropy](https://mlsanity.com/paper/2401.01268/) (2024)

## Abstract (arXiv)

Performance in face and speaker verification is largely driven by margin-penalty softmax losses such as CosFace and ArcFace. Recently introduced α-divergence loss functions offer a compelling alternative, particularly due to their ability to induce sparse solutions (when α>1). However, standard geometric margins are designed for the softmax function and do not naturally extend to this generalized probabilistic framework. In this paper we propose Q-Margin, a novel α-divergence loss that introduces a principled probabilistic margin. Unlike conventional methods that apply geometric penalties to the logits (unnormalized log-likelihoods), Q-Margin encodes the margin penalty directly into the reference measure (prior probabilities). This formulation naturally encourages discriminative embeddings while preserving the beneficial sparsity properties of the α-divergence. We demonstrate that Q-Margin achieves competitive or superior performance on the challenging IJB-B and IJB-C face verification benchmarks and similarly strong results in speaker verification on VoxCeleb. Crucially, against ArcFace and CosFace baselines trained under an identical recipe, Q-Margin consistently improves at low False Acceptance Rates (FARs), a capability critical for practical high-security applications. Finally, the extreme sparsity of the Q-Margin posteriors enables exact and memory-efficient training, offering a scalable solution for datasets with millions of identities.