# OTFace: Hard Samples Guided Optimal Transport Loss for Deep Face Representation

arXiv: https://arxiv.org/abs/2203.14461 · HTML: https://mlsanity.com/paper/2203.14461/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 74 references that are in the map.
- First posted on arXiv 28 Mar 2022.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [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)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [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)
- [The MegaFace Benchmark: 1 Million Faces for Recognition at Scale](https://mlsanity.com/paper/1512.00596/) (2015)
- [MobileFaceNets: Efficient CNNs for Accurate Real-Time Face Verification on Mobile Devices](https://mlsanity.com/paper/1804.07573/) (2018)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [AdaCos: Adaptively Scaling Cosine Logits for Effectively Learning Deep Face Representations](https://mlsanity.com/paper/1905.00292/) (2019)
- [DeepID3: Face Recognition with Very Deep Neural Networks](https://mlsanity.com/paper/1502.00873/) (2015)
- [Mis-classified Vector Guided Softmax Loss for Face Recognition](https://mlsanity.com/paper/1912.00833/) (2019)
- [Towards Interpretable Deep Metric Learning with Structural Matching](https://mlsanity.com/paper/2108.05889/) (2021)
- [Wasserstein Discriminant Analysis](https://mlsanity.com/paper/1608.08063/) (2016)
- [Noisy Softmax: Improving the Generalization Ability of DCNN via Postponing the Early Softmax Saturation](https://mlsanity.com/paper/1708.03769/) (2017)
- [DeepFace-EMD: Re-ranking Using Patch-wise Earth Mover's Distance Improves Out-Of-Distribution Face Identification](https://mlsanity.com/paper/2112.04016/) (2021)
- [Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes](https://mlsanity.com/paper/1405.1207/) (2014)

## Built on by (most cited first, 2 of 2)

- [Learning with Imbalanced Noisy Data by Preventing Bias in Sample Selection](https://mlsanity.com/paper/2402.11242/) (2024)
- [SWT: Self-Supervised Video Object Segmentation via Sliding, Wavelet and Transportation](https://mlsanity.com/paper/2609.31725/) (2026)

## Abstract (arXiv)

Face representation in the wild is extremely hard due to the large scale face variations. To this end, some deep convolutional neural networks (CNNs) have been developed to learn discriminative feature by designing properly margin-based losses, which perform well on easy samples but fail on hard samples. Based on this, some methods mainly adjust the weights of hard samples in training stage to improve the feature discrimination. However, these methods overlook the feature distribution property which may lead to better results since the miss-classified hard samples may be corrected by using the distribution metric. This paper proposes the hard samples guided optimal transport (OT) loss for deep face representation, OTFace for short. OTFace aims to enhance the performance of hard samples by introducing the feature distribution discrepancy while maintain the performance on easy samples. Specifically, we embrace triplet scheme to indicate hard sample groups in one mini-batch during training. OT is then used to characterize the distribution differences of features from the high level convolutional layer. Finally, we integrate the margin-based-softmax (e.g. ArcFace or AM-Softmax) and OT to guide deep CNN learning. Extensive experiments are conducted on several benchmark databases. The quantitative results demonstrate the advantages of the proposed OTFace over state-of-the-art methods.