{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:17:39Z","timestamp":1778084259177,"version":"3.51.4"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T00:00:00Z","timestamp":1771891200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach Learn"],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s10994-025-06987-8","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T08:34:41Z","timestamp":1771922081000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dual-granularity Sinkhorn Distillation for Enhanced Learning from Long-Tailed Noisy Data"],"prefix":"10.1007","volume":"115","author":[{"given":"Feng","family":"Hong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Huang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zihua","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhihan","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiangchao","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongsheng","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanfeng","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,24]]},"reference":[{"key":"6987_CR1","unstructured":"Ahn, S., Ko, J., & Yun, S. (2023). CUDA: Curriculum of data augmentation for long-tailed recognition. In: ICLR."},{"key":"6987_CR2","unstructured":"Bhardwaj, R., Vaidya, T., & Poria, S. (2022). KNOT: Knowledge distillation using optimal transport for solving NLP tasks, pp. 4801\u20134820."},{"key":"6987_CR3","unstructured":"Cao, K., Chen, Y., Lu, J., Ar\u00e9chiga, N., Gaidon, A., & Ma, T. (2021). Heteroskedastic and imbalanced deep learning with adaptive regularization. In: ICLR."},{"key":"6987_CR4","unstructured":"Cao, K., Wei, C., Gaidon, A., Ar\u00e9chiga, N., & Ma, T. (2019). Learning imbalanced datasets with label-distribution-aware margin loss (LDAM). In: NeurIPS, pp. 1565\u20131576."},{"key":"6987_CR5","unstructured":"Caron, M., Misra, I., Mairal, J., Goyal, P., Bojanowski, P., & Joulin, A. (2020). Unsupervised learning of visual features by contrasting cluster assignments. In: NeurIPS."},{"key":"6987_CR6","doi-asserted-by":"crossref","unstructured":"Caron, M., Touvron, H., Misra, I., J\u00e9gou, H., Mairal, J., Bojanowski, P., & Joulin, A. (2021). Emerging properties in self-supervised vision transformers. In: ICCV, pp. 9630\u20139640.","DOI":"10.1109\/ICCV48922.2021.00951"},{"key":"6987_CR7","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1613\/jair.953","volume":"16","author":"NV Chawla","year":"2002","unstructured":"Chawla, N. V., Bowyer, K. W., Hall, L. O., & Kegelmeyer, W. P. (2002). SMOTE: Synthetic minority over-sampling technique. Journal of Artificial Intelligence Research,16, 321\u2013357.","journal-title":"Journal of Artificial Intelligence Research"},{"key":"6987_CR8","doi-asserted-by":"crossref","unstructured":"Cui, Y., Jia, M., Lin, T., Song, Y., & Belongie, S. J. (2019). Class-balanced loss based on effective number of samples. In: CVPR, pp. 9268\u20139277.","DOI":"10.1109\/CVPR.2019.00949"},{"key":"6987_CR9","unstructured":"Cuturi, M. (2013). Sinkhorn distances: Lightspeed computation of optimal transport. In: NeurIPS, pp. 2292\u20132300."},{"key":"6987_CR10","doi-asserted-by":"crossref","unstructured":"Deng, J., Dong, W., Socher, R., Li, L., Li, K., & Fei-Fei, L. (2009). Imagenet: A large-scale hierarchical image database. In: CVPR, pp. 248\u2013255.","DOI":"10.1109\/CVPR.2009.5206848"},{"key":"6987_CR11","doi-asserted-by":"crossref","unstructured":"Devlin, J., Chang, M., Lee, K., & Toutanova, K. (2019). BERT: Pre-training of deep bidirectional transformers for language understanding, pp. 4171\u20134186.","DOI":"10.18653\/v1\/N19-1423"},{"key":"6987_CR12","unstructured":"Foret, P., Kleiner, A., Mobahi, H., & Neyshabur, B. (2021). Sharpness-aware minimization for efficiently improving generalization. In: ICLR."},{"key":"6987_CR13","unstructured":"Han, B., Yao, Q., Yu, X., Niu, G., Xu, M., Hu, W., Tsang, I. W., & Sugiyama, M. (2018) Co-teaching: Robust training of deep neural networks with extremely noisy labels. In: NeurIPS, pp. 8536\u20138546."},{"key":"6987_CR14","first-page":"4006","volume":"119","author":"B Han","year":"2020","unstructured":"Han, B., Niu, G., Yu, X., Yao, Q., Xu, M., Tsang, I. W., & Sugiyama, M. (2020). SIGUA: Forgetting may make learning with noisy labels more robust. Proceedings of Machine Learning Research,119, 4006\u20134016.","journal-title":"Proceedings of Machine Learning Research"},{"key":"6987_CR15","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep residual learning for image recognition. In: CVPR, pp. 770\u2013778.","DOI":"10.1109\/CVPR.2016.90"},{"key":"6987_CR16","doi-asserted-by":"crossref","unstructured":"Huang, Y., Bai, B., Zhao, S., Bai, K., & Wang, F. (2022). Uncertainty-aware learning against label noise on imbalanced datasets. In: AAAI, pp. 6960\u20136969.","DOI":"10.1609\/aaai.v36i6.20654"},{"key":"6987_CR17","unstructured":"Jiang, L., Huang, D., Liu, M., & Yang, W. (2020). Beyond synthetic noise: Deep learning on controlled noisy labels. 119, 4804\u20134815."},{"key":"6987_CR18","unstructured":"Kang, B., Li, Y., Xie, S., Yuan, Z., & Feng, J. (2021). Exploring balanced feature spaces for representation learning. In: ICLR."},{"key":"6987_CR19","unstructured":"Kang, B., Xie, S., Rohrbach, M., Yan, Z., Gordo, A., Feng, J., & Kalantidis, Y. (2020). Decoupling representation and classifier for long-tailed recognition. In: ICLR."},{"key":"6987_CR20","doi-asserted-by":"crossref","unstructured":"Karim, N., Rizve, M. N., Rahnavard, N., Mian, A., & Shah, M. (2022). UNICON: Combating label noise through uniform selection and contrastive learning. In: CVPR, pp. 9666\u20139676.","DOI":"10.1109\/CVPR52688.2022.00945"},{"key":"6987_CR21","unstructured":"Krizhevsky, A. (2009). Learning multiple layers of features from tiny images."},{"key":"6987_CR22","doi-asserted-by":"crossref","unstructured":"Li, Y., Chen, Y., Yu, X., Chen, D., & Shen, X. (2024). SURE: Survey recipes for building reliable and robust deep networks. CoRR. arXiv:abs\/2403.00543","DOI":"10.1109\/CVPR52733.2024.01657"},{"key":"6987_CR23","unstructured":"Li, X., Liu, T., Han, B., Niu, G., & Sugiyama, M. (2021). Provably end-to-end label-noise learning without anchor points, pp. 6403\u20136413."},{"key":"6987_CR24","unstructured":"Li, J., Socher, R., & Hoi, S. C. H. (2020). Dividemix: Learning with noisy labels as semi-supervised learning. In: ICLR."},{"key":"6987_CR25","unstructured":"Li, W., Wang, L., Li, W., Agustsson, E., & Gool, L. V. (2017). Webvision database: Visual learning and understanding from web data. CoRR. arXiv:abs\/1708.02862"},{"key":"6987_CR26","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.media.2017.07.005","volume":"42","author":"G Litjens","year":"2017","unstructured":"Litjens, G., Kooi, T., Bejnordi, B. E., Setio, A. A. A., Ciompi, F., Ghafoorian, M., Laak, J. A. W. M., Ginneken, B., & S\u00e1nchez, C. I. (2017). A survey on deep learning in medical image analysis. Medical Image Analysis,42, 60\u201388.","journal-title":"Medical Image Analysis"},{"key":"6987_CR27","unstructured":"Liu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., & Stoyanov, V. (2019). Roberta: A robustly optimized BERT pretraining approach. CoRR. arXiv:abs\/1907.11692"},{"key":"6987_CR28","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.neucom.2020.07.048","volume":"415","author":"Y Liu","year":"2020","unstructured":"Liu, Y., Zhang, W., & Wang, J. (2020). Adaptive multi-teacher multi-level knowledge distillation. Neurocomputing,415, 106\u2013113.","journal-title":"Neurocomputing"},{"key":"6987_CR29","doi-asserted-by":"crossref","unstructured":"Lu, Y., Zhang, Y., Han, B., Cheung, Y., & Wang, H. (2023). Label-noise learning with intrinsically long-tailed data. In: ICCV, pp. 1369\u20131378.","DOI":"10.1109\/ICCV51070.2023.00132"},{"key":"6987_CR30","unstructured":"Menon, A. K., Jayasumana, S., Rawat, A. S., Jain, H., Veit, A., & Kumar, S. (2021). Long-tail learning via logit adjustment. In: ICLR."},{"key":"6987_CR31","unstructured":"Monge, G. (1781). M\u00e9moire sur la Th\u00e9orie des D\u00e9blais Et des remblais."},{"key":"6987_CR32","doi-asserted-by":"crossref","unstructured":"Park, S., Lim, J., Jeon, Y., & Choi, J. Y. (2021). Influence-balanced loss for imbalanced visual classification. In: ICCV, pp. 715\u2013724.","DOI":"10.1109\/ICCV48922.2021.00077"},{"key":"6987_CR33","doi-asserted-by":"crossref","unstructured":"Pham, C., Hoang, T., & Do, T. (2023). Collaborative multi-teacher knowledge distillation for learning low bit-width deep neural networks, pp. 6424\u20136432.","DOI":"10.1109\/WACV56688.2023.00637"},{"key":"6987_CR34","unstructured":"Ren, J., Yu, C., Sheng, S., Ma, X., Zhao, H., Yi, S., & Li, H. (2020). Balanced meta-softmax for long-tailed visual recognition. In: NeurIPS."},{"key":"6987_CR35","first-page":"228","volume":"18","author":"B Rooyen","year":"2017","unstructured":"Rooyen, B., & Williamson, R. C. (2017). A theory of learning with corrupted labels. Journal of Machine Learning Research,18, 228\u2013122850.","journal-title":"Journal of Machine Learning Research"},{"key":"6987_CR36","doi-asserted-by":"crossref","unstructured":"Santambrogio, F. (2015). Optimal transport for applied mathematicians: Calculus of variations, PDEs, and modeling. Progress in Nonlinear Differential Equations and Their Applications.","DOI":"10.1007\/978-3-319-20828-2"},{"key":"6987_CR37","unstructured":"Shu, J., Xie, Q., Yi, L., Zhao, Q., Zhou, S., Xu, Z., & Meng, D. (2019). Meta-weight-net: Learning an explicit mapping for sample weighting. In: NeurIPS, pp. 1917\u20131928."},{"issue":"11","key":"6987_CR38","doi-asserted-by":"publisher","first-page":"8135","DOI":"10.1109\/TNNLS.2022.3152527","volume":"34","author":"H Song","year":"2023","unstructured":"Song, H., Kim, M., Park, D., Shin, Y., & Lee, J. (2023). Learning from noisy labels with deep neural networks: A survey. IEEE Transactions on Neural Networks and Learning Systems,34(11), 8135\u20138153.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"6987_CR39","doi-asserted-by":"crossref","unstructured":"Tan, X., Ren, Y., He, D., Qin, T., Zhao, Z., & Liu, T. (2019). Multilingual neural machine translation with knowledge distillation. In: ICLR.","DOI":"10.18653\/v1\/D19-1089"},{"key":"6987_CR40","unstructured":"Wei, T., Shi, J., Tu, W., & Li, Y. (2021). Robust long-tailed learning under label noise. CoRR. arXiv:abs\/2108.11569"},{"key":"6987_CR41","unstructured":"Wei, J., Zhu, Z., Cheng, H., Liu, T., Niu, G., & Liu, Y. (2022). Learning with noisy labels revisited: A study using real-world human annotations. In: ICLR."},{"key":"6987_CR42","unstructured":"Wei, J., Zhu, Z., Niu, G., Liu, T., Liu, S., Sugiyama, M., & Liu, Y. (2023). Fairness improves learning from noisily labeled long-tailed data. CoRR. arXiv:abs\/2303.12291"},{"key":"6987_CR43","doi-asserted-by":"crossref","unstructured":"Wu, T., Liu, Z., Huang, Q., Wang, Y., & Lin, D. (2021). Adversarial robustness under long-tailed distribution. In: CVPR, pp. 8659\u20138668.","DOI":"10.1109\/CVPR46437.2021.00855"},{"key":"6987_CR44","doi-asserted-by":"crossref","unstructured":"Xiao, T., Xia, T., Yang, Y., Huang, C., & Wang, X. (2015). Learning from massive noisy labeled data for image classification. In: CVPR, pp. 2691\u20132699.","DOI":"10.1109\/CVPR.2015.7298885"},{"key":"6987_CR45","unstructured":"Yang, Z., Xu, Q., Wang, Z., Li, S., Han, B., Bao, S., Cao, X., & Huang, Q. (2024). Harnessing hierarchical label distribution variations in test agnostic long-tail recognition. CoRR. arXiv:abs\/2405.07780"},{"key":"6987_CR46","doi-asserted-by":"crossref","unstructured":"Yao, Y., Sun, Z., Zhang, C., Shen, F., Wu, Q., Zhang, J., & Tang, Z. (2021). Jo-SRC: A contrastive approach for combating noisy labels. In: CVPR, pp. 5192\u20135201.","DOI":"10.1109\/CVPR46437.2021.00515"},{"key":"6987_CR47","doi-asserted-by":"crossref","unstructured":"Yi, X., Tang, K., Hua, X., Lim, J., & Zhang, H. (2022). Identifying hard noise in long-tailed sample distribution. ECCV. Lecture Notes in Computer Science, 13686, 739\u2013756.","DOI":"10.1007\/978-3-031-19809-0_42"},{"key":"6987_CR48","doi-asserted-by":"crossref","unstructured":"Zhang, S., Li, Z., Yan, S., He, X., & Sun, J. (2021). Distribution alignment: A unified framework for long-tail visual recognition. In: CVPR, pp. 2361\u20132370.","DOI":"10.1109\/CVPR46437.2021.00239"},{"key":"6987_CR49","doi-asserted-by":"crossref","unstructured":"Zhang, M., Zhao, X., Yao, J., Yuan, C., & Huang, W. (2023). When noisy labels meet long tail dilemmas: A representation calibration method. In: ICCV, pp. 15844\u201315854.","DOI":"10.1109\/ICCV51070.2023.01456"},{"issue":"9","key":"6987_CR50","doi-asserted-by":"publisher","first-page":"10795","DOI":"10.1109\/TPAMI.2023.3268118","volume":"45","author":"Y Zhang","year":"2023","unstructured":"Zhang, Y., Kang, B., Hooi, B., Yan, S., & Feng, J. (2023). Deep long-tailed learning: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence,45(9), 10795\u201310816.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"}],"container-title":["Machine Learning"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-025-06987-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10994-025-06987-8","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10994-025-06987-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T15:35:10Z","timestamp":1778081710000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10994-025-06987-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,24]]},"references-count":50,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["6987"],"URL":"https:\/\/doi.org\/10.1007\/s10994-025-06987-8","relation":{},"ISSN":["0885-6125","1573-0565"],"issn-type":[{"value":"0885-6125","type":"print"},{"value":"1573-0565","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,24]]},"assertion":[{"value":"29 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 March 2026","order":6,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":7,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The original online version of this article was revised: The editor information in the article note has been corrected.","order":8,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no financial or non-financial interests to disclose that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}],"article-number":"41"}}