# SoLar: Sinkhorn Label Refinery for Imbalanced Partial-Label Learning

arXiv: https://arxiv.org/abs/2209.10365 · HTML: https://mlsanity.com/paper/2209.10365/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 30 of 37)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Long-tailed Recognition by Routing Diverse Distribution-Aware Experts](https://mlsanity.com/paper/2010.01809/) (2020)
- [Long-Tailed Classification by Keeping the Good and Removing the Bad Momentum Causal Effect](https://mlsanity.com/paper/2009.12991/) (2020)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [OTA: Optimal Transport Assignment for Object Detection](https://mlsanity.com/paper/2103.14259/) (2021)
- [CReST: A Class-Rebalancing Self-Training Framework for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2102.09559/) (2021)
- [Overcoming Classifier Imbalance for Long-tail Object Detection with Balanced Group Softmax](https://mlsanity.com/paper/2006.10408/) (2020)
- [M2m: Imbalanced Classification via Major-to-minor Translation](https://mlsanity.com/paper/2004.00431/) (2020)
- [Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2007.08844/) (2020)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [Optimal Transport for Multi-source Domain Adaptation under Target Shift](https://mlsanity.com/paper/1803.04899/) (2018)
- [Leveraged Weighted Loss for Partial Label Learning](https://mlsanity.com/paper/2106.05731/) (2021)
- [Learning with Multiple Complementary Labels](https://mlsanity.com/paper/1912.12927/) (2019)
- [Heteroskedastic and Imbalanced Deep Learning with Adaptive Regularization](https://mlsanity.com/paper/2006.15766/) (2020)
- [Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2110.12911/) (2021)

## Built on by (most cited first, 30 of 31)

- [ARGS: Alignment as Reward-Guided Search](https://mlsanity.com/paper/2402.01694/) (2024)
- [Process Reward Model with Q-Value Rankings](https://mlsanity.com/paper/2410.11287/) (2024)
- [Multi-granularity Correspondence Learning from Long-term Noisy Videos](https://mlsanity.com/paper/2401.16702/) (2024)
- [Long-Tailed Partial Label Learning via Dynamic Rebalancing](https://mlsanity.com/paper/2302.05080/) (2023)
- [CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels](https://mlsanity.com/paper/2312.06221/) (2023)
- [CroSel: Cross Selection of Confident Pseudo Labels for Partial-Label Learning](https://mlsanity.com/paper/2303.10365/) (2023)
- [Learning to Rematch Mismatched Pairs for Robust Cross-Modal Retrieval](https://mlsanity.com/paper/2403.05105/) (2024)
- [Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty](https://mlsanity.com/paper/2404.10980/) (2024)
- [Disambiguated Attention Embedding for Multi-Instance Partial-Label Learning](https://mlsanity.com/paper/2305.16912/) (2023)
- [Active Learning for Semantic Segmentation with Multi-class Label Query](https://mlsanity.com/paper/2309.09319/) (2023)
- [NLPrompt: Noise-Label Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2412.01256/) (2024)
- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)
- [On the Learnability of Out-of-distribution Detection](https://mlsanity.com/paper/2404.04865/) (2024)
- [Robust Representation Learning with Reliable Pseudo-labels Generation via Self-Adaptive Optimal Transport for Short Text Clustering](https://mlsanity.com/paper/2305.16335/) (2023)
- [Controller-Guided Partial Label Consistency Regularization with Unlabeled Data](https://mlsanity.com/paper/2210.11194/) (2022)
- [Robust Representation Learning for Unreliable Partial Label Learning](https://mlsanity.com/paper/2308.16718/) (2023)
- [Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies](https://mlsanity.com/paper/2407.10000/) (2024)
- [Prior2Posterior: Model Prior Correction for Long-Tailed Learning](https://mlsanity.com/paper/2412.16540/) (2024)
- [Tuning the Right Foundation Models is What you Need for Partial Label Learning](https://mlsanity.com/paper/2506.05027/) (2025)
- [OTTER: Effortless Label Distribution Adaptation of Zero-shot Models](https://mlsanity.com/paper/2404.08461/) (2024)
- [Prototype-based Optimal Transport for Out-of-Distribution Detection](https://mlsanity.com/paper/2410.07617/) (2024)
- [Pseudo Labels Regularization for Imbalanced Partial-Label Learning](https://mlsanity.com/paper/2303.03946/) (2023)
- [Partial-label Learning with Mixed Closed-set and Open-set Out-of-candidate Examples](https://mlsanity.com/paper/2307.00553/) (2023)
- [A Unified Optimal Transport Framework for Cross-Modal Retrieval with Noisy Labels](https://mlsanity.com/paper/2403.13480/) (2024)
- [Towards Robust Incremental Learning under Ambiguous Supervision](https://mlsanity.com/paper/2501.13584/) (2025)
- [Exploiting the Potential Supervision Information of Clean Samples in Partial Label Learning](https://mlsanity.com/paper/2505.09354/) (2025)
- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)
- [Noise-aware few-shot learning through bi-directional multi-view prompt alignment](https://mlsanity.com/paper/2603.11617/) (2026)
- [Holistic Optimal Label Selection for Robust Prompt Learning under Partial Labels](https://mlsanity.com/paper/2604.06614/) (2026)
- [Embracing Biased Transition Matrices for Complementary-Label Learning with Many Classes](https://mlsanity.com/paper/2605.15586/) (2026)

## Abstract (arXiv)

Partial-label learning (PLL) is a peculiar weakly-supervised learning task where the training samples are generally associated with a set of candidate labels instead of single ground truth. While a variety of label disambiguation methods have been proposed in this domain, they normally assume a class-balanced scenario that may not hold in many real-world applications. Empirically, we observe degenerated performance of the prior methods when facing the combinatorial challenge from the long-tailed distribution and partial-labeling. In this work, we first identify the major reasons that the prior work failed. We subsequently propose SoLar, a novel Optimal Transport-based framework that allows to refine the disambiguated labels towards matching the marginal class prior distribution. SoLar additionally incorporates a new and systematic mechanism for estimating the long-tailed class prior distribution under the PLL setup. Through extensive experiments, SoLar exhibits substantially superior results on standardized benchmarks compared to the previous state-of-the-art PLL methods. Code and data are available at: https://github.com/hbzju/SoLar .