# Sinkhorn Label Allocation: Semi-Supervised Classification via Annealed Self-Training

arXiv: https://arxiv.org/abs/2102.08622 · HTML: https://mlsanity.com/paper/2102.08622/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 54 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 19 of 19)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Self-training with Noisy Student improves ImageNet classification](https://mlsanity.com/paper/1911.04252/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Regularization With Stochastic Transformations and Perturbations for Deep Semi-Supervised Learning](https://mlsanity.com/paper/1606.04586/) (2016)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Learning with Pseudo-Ensembles](https://mlsanity.com/paper/1412.4864/) (2014)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [Deep multi-class learning from label proportions](https://mlsanity.com/paper/1905.12909/) (2019)

## Built on by (most cited first, 30 of 32)

- [SoftMatch: Addressing the Quantity-Quality Trade-off in Semi-supervised Learning](https://mlsanity.com/paper/2301.10921/) (2023)
- [Improved Regularization and Robustness for Fine-tuning in Neural Networks](https://mlsanity.com/paper/2111.04578/) (2021)
- [SoLar: Sinkhorn Label Refinery for Imbalanced Partial-Label Learning](https://mlsanity.com/paper/2209.10365/) (2022)
- [Instance-specific and Model-adaptive Supervision for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2211.11335/) (2022)
- [Face.evoLVe: A High-Performance Face Recognition Library](https://mlsanity.com/paper/2107.08621/) (2021)
- [MutexMatch: Semi-Supervised Learning with Mutex-Based Consistency Regularization](https://mlsanity.com/paper/2203.14316/) (2022)
- [CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels](https://mlsanity.com/paper/2312.06221/) (2023)
- [P2OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering](https://mlsanity.com/paper/2401.09266/) (2024)
- [Towards Semi-supervised Learning with Non-random Missing Labels](https://mlsanity.com/paper/2308.08872/) (2023)
- [Learning to Rematch Mismatched Pairs for Robust Cross-Modal Retrieval](https://mlsanity.com/paper/2403.05105/) (2024)
- [Dual-level Adaptive Self-Labeling for Novel Class Discovery in Point Cloud Segmentation](https://mlsanity.com/paper/2407.12489/) (2024)
- [MaxMatch: Semi-Supervised Learning with Worst-Case Consistency](https://mlsanity.com/paper/2209.12611/) (2022)
- [Roll With the Punches: Expansion and Shrinkage of Soft Label Selection for Semi-supervised Fine-Grained Learning](https://mlsanity.com/paper/2312.12237/) (2023)
- [OTMatch: Improving Semi-Supervised Learning with Optimal Transport](https://mlsanity.com/paper/2310.17455/) (2023)
- [Enhancing Sample Utilization through Sample Adaptive Augmentation in Semi-Supervised Learning](https://mlsanity.com/paper/2309.03598/) (2023)
- [Confident Sinkhorn Allocation for Pseudo-Labeling](https://mlsanity.com/paper/2206.05880/) (2022)
- [You can't handle the (dirty) truth: Data-centric insights improve pseudo-labeling](https://mlsanity.com/paper/2406.13733/) (2024)
- [SP2OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering](https://mlsanity.com/paper/2404.03446/) (2024)
- [RoNID: New Intent Discovery with Generated-Reliable Labels and Cluster-friendly Representations](https://mlsanity.com/paper/2404.08977/) (2024)
- [Towards Real-world Scenario: Imbalanced New Intent Discovery](https://mlsanity.com/paper/2406.03127/) (2024)
- [PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering](https://mlsanity.com/paper/2506.12408/) (2025)
- [Supervise Less, See More: Training-free Nuclear Instance Segmentation with Prototype-Guided Prompting](https://mlsanity.com/paper/2511.19953/) (2025)
- [OTTER: Effortless Label Distribution Adaptation of Zero-shot Models](https://mlsanity.com/paper/2404.08461/) (2024)
- [Less is More: Pseudo-Label Filtering for Continual Test-Time Adaptation](https://mlsanity.com/paper/2406.02609/) (2024)
- [Rethinking Multiple Instance Learning: Developing an Instance-Level Classifier via Weakly-Supervised Self-Training](https://mlsanity.com/paper/2408.04813/) (2024)
- [Taming Overconfident Prediction on Unlabeled Data from Hindsight](https://mlsanity.com/paper/2112.08200/) (2021)
- [SiMCa: Sinkhorn Matrix Factorization with Capacity Constraints](https://mlsanity.com/paper/2203.10107/) (2022)
- [A Unified Optimal Transport Framework for Cross-Modal Retrieval with Noisy Labels](https://mlsanity.com/paper/2403.13480/) (2024)
- [An Adaptor for Triggering Semi-Supervised Learning to Out-of-Box Serve Deep Image Clustering](https://mlsanity.com/paper/2509.20976/) (2025)
- [What Makes Synthetic Data Effective in Image Segmentation](https://mlsanity.com/paper/2605.19289/) (2026)

## Abstract (arXiv)

Self-training is a standard approach to semi-supervised learning where the learner's own predictions on unlabeled data are used as supervision during training. In this paper, we reinterpret this label assignment process as an optimal transportation problem between examples and classes, wherein the cost of assigning an example to a class is mediated by the current predictions of the classifier. This formulation facilitates a practical annealing strategy for label assignment and allows for the inclusion of prior knowledge on class proportions via flexible upper bound constraints. The solutions to these assignment problems can be efficiently approximated using Sinkhorn iteration, thus enabling their use in the inner loop of standard stochastic optimization algorithms. We demonstrate the effectiveness of our algorithm on the CIFAR-10, CIFAR-100, and SVHN datasets in comparison with FixMatch, a state-of-the-art self-training algorithm. Our code is available at https://github.com/stanford-futuredata/sinkhorn-label-allocation.