# CSOT: Curriculum and Structure-Aware Optimal Transport for Learning with Noisy Labels

arXiv: https://arxiv.org/abs/2312.06221 · HTML: https://mlsanity.com/paper/2312.06221/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 87 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 30 of 53)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning](https://mlsanity.com/paper/2205.07246/) (2022)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise](https://mlsanity.com/paper/1802.05300/) (2018)

## Built on by (most cited first, 17 of 17)

- [Global and Local Prompts Cooperation via Optimal Transport for Federated Learning](https://mlsanity.com/paper/2403.00041/) (2024)
- [Learning Clustering-based Prototypes for Compositional Zero-shot Learning](https://mlsanity.com/paper/2502.06501/) (2025)
- [P2OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering](https://mlsanity.com/paper/2401.09266/) (2024)
- [SOOD++: Leveraging Unlabeled Data to Boost Oriented Object Detection](https://mlsanity.com/paper/2407.01016/) (2024)
- [NLPrompt: Noise-Label Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2412.01256/) (2024)
- [A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributions](https://mlsanity.com/paper/2405.03664/) (2024)
- [SP2OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering](https://mlsanity.com/paper/2404.03446/) (2024)
- [MADPOT: Medical Anomaly Detection with CLIP Adaptation and Partial Optimal Transport](https://mlsanity.com/paper/2507.06733/) (2025)
- [Reliable Pseudo-labeling via Optimal Transport with Attention for Short Text Clustering](https://mlsanity.com/paper/2501.15194/) (2025)
- [Learning to Forget with Information Divergence Reweighted Objectives for Noisy Labels](https://mlsanity.com/paper/2508.06622/) (2025)
- [Self-Ensemble Post Learning for Noisy Domain Generalization](https://mlsanity.com/paper/2512.10818/) (2025)
- [Deep Probabilistic Supervision for Image Classification](https://mlsanity.com/paper/2512.24162/) (2025)
- [Structure-aware Prompt Adaptation from Seen to Unseen for Open-Vocabulary Compositional Zero-Shot Learning](https://mlsanity.com/paper/2603.03815/) (2026)
- [Noise-aware few-shot learning through bi-directional multi-view prompt alignment](https://mlsanity.com/paper/2603.11617/) (2026)
- [Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration](https://mlsanity.com/paper/2605.06260/) (2026)
- [TecoPrompt: Temporal-Conservative Prompt Learning for Vision-Language Models](https://mlsanity.com/paper/2609.16858/) (2026)
- [GERIS: A Game-Theoretic Framework for Filtering Instance-Dependent Label Noise in License Plate Data Augmentation](https://mlsanity.com/paper/2609.31731/) (2026)

## Abstract (arXiv)

Learning with noisy labels (LNL) poses a significant challenge in training a well-generalized model while avoiding overfitting to corrupted labels. Recent advances have achieved impressive performance by identifying clean labels and correcting corrupted labels for training. However, the current approaches rely heavily on the model's predictions and evaluate each sample independently without considering either the global and local structure of the sample distribution. These limitations typically result in a suboptimal solution for the identification and correction processes, which eventually leads to models overfitting to incorrect labels. In this paper, we propose a novel optimal transport (OT) formulation, called Curriculum and Structure-aware Optimal Transport (CSOT). CSOT concurrently considers the inter- and intra-distribution structure of the samples to construct a robust denoising and relabeling allocator. During the training process, the allocator incrementally assigns reliable labels to a fraction of the samples with the highest confidence. These labels have both global discriminability and local coherence. Notably, CSOT is a new OT formulation with a nonconvex objective function and curriculum constraints, so it is not directly compatible with classical OT solvers. Here, we develop a lightspeed computational method that involves a scaling iteration within a generalized conditional gradient framework to solve CSOT efficiently. Extensive experiments demonstrate the superiority of our method over the current state-of-the-arts in LNL. Code is available at https://github.com/changwxx/CSOT-for-LNL.