{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T07:11:46Z","timestamp":1780470706247,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We introduce the symmetric co-skewness moment (SCKM)\u2014a third-order informational dissimilarity metric that consistently outperforms state-of-the-art client-selection heuristics in federated learning (FL) under heterogeneous data. Unlike similarity-driven schemes, SCKM minimizes redundancy by favoring clients with complementary gradients, delivering faster and more stable convergence even at high heterogeneity levels. Operating on highly compressed 0.5% gradient summaries, our framework provides two operating modes for different deployment scales: (i) SCKM-Select directly ranks and schedules a small candidate pool, whereas (ii) SCKM-Cluster adds a fast, elbow-guided clustering step to scalably choose from thousands of users. We evaluate both variants on a VGG-16 model across multiple non-IID partition schemes and initializations, observing consistent gains over leading cosine-similarity, loss-sketch, and max-diversity baselines\u2014without increasing the communication budget.<\/jats:p>","DOI":"10.3390\/e28060630","type":"journal-article","created":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:17:31Z","timestamp":1780467451000},"page":"630","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SCKM: Symmetric Co-Skew Moment for User Selection in Federated Learning"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6824-7291","authenticated-orcid":false,"given":"Liangyan","family":"Li","sequence":"first","affiliation":[{"name":"Huawei Technologies Co., Ltd., Waterloo, ON N2J 4PP, Canada"},{"name":"Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7366-724X","authenticated-orcid":false,"given":"Yangyi","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yimo","family":"Ning","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Toronto, Toronto, ON M5S 1A1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefano","family":"Rini","sequence":"additional","affiliation":[{"name":"Department of Electronics and Electrical Engineering, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8084-9332","authenticated-orcid":false,"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, McMaster University, Hamilton, ON L8S 4L8, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"ref_1","unstructured":"McMahan, B., Moore, E., Ramage, D., Hampson, S., and y Arcas, B.A. (2017, January 20\u201322). Communication-efficient learning of deep networks from decentralized data. Proceedings of the Artificial Intelligence and Statistics, Ft. Lauderdale, FL, USA."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, H., Kaplan, Z., Niu, D., and Li, B. (2020, January 6\u20139). Optimizing federated learning on non-iid data with reinforcement learning. Proceedings of the IEEE INFOCOM 2020-IEEE Conference on Computer Communications, Toronto, ON, Canada.","DOI":"10.1109\/INFOCOM41043.2020.9155494"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ribero, M., and Vikalo, H. (2020). Communication-efficient federated learning via optimal client sampling. arXiv.","DOI":"10.52591\/lxai2020071310"},{"key":"ref_4","unstructured":"Cho, Y.J., Wang, J., and Joshi, G. (2020). Client selection in federated learning: Convergence analysis and power-of-choice selection strategies. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Xu, J., Chen, Z., Quek, T.Q., and Chong, K.F.E. (2022, January 19\u201320). Fedcorr: Multi-stage federated learning for label noise correction. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.00994"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000083","article-title":"Advances and open problems in federated learning","volume":"14","author":"Kairouz","year":"2021","journal-title":"Found. Trends\u00ae Mach. Learn."},{"key":"ref_7","unstructured":"Zhang, J., Li, Z., Li, B., Xu, J., Wu, S., Ding, S., and Wu, C. (2022, January 17\u201323). Federated learning with label distribution skew via logits calibration. Proceedings of the International Conference on Machine Learning, Baltimore, MD, USA."},{"key":"ref_8","unstructured":"McMahan, B., and Ramage, D. (2026, May 24). Federated Learning: Collaborative Machine Learning without Centralized Training Data. Google Research Blog, Available online: https:\/\/research.google\/blog\/federated-learning-collaborative-machine-learning-without-centralized-training-data\/."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3710","DOI":"10.1109\/TNNLS.2020.3015958","article-title":"Clustered federated learning: Model-agnostic distributed multitask optimization under privacy constraints","volume":"32","author":"Sattler","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Nishio, T., and Yonetani, R. (2019). Client selection for federated learning with heterogeneous resources in mobile edge. Proceedings of the ICC 2019-2019 IEEE International Conference on Communications (ICC), IEEE.","DOI":"10.1109\/ICC.2019.8761315"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Marnissi, O., Hammouti, H.E., and Bergou, E.H. (2024). Client selection in federated learning based on gradients importance. Proceedings of the AIP Conference Proceedings, AIP Publishing.","DOI":"10.1063\/5.0194687"},{"key":"ref_12","unstructured":"Liu, R., Cao, Y., Yoshikawa, M., and Chen, H. (2020). Fedsel: Federated sgd under local differential privacy with top-k dimension selection. Proceedings of the Database Systems for Advanced Applications: 25th International Conference, DASFAA 2020, Jeju, Republic of Korea, 24\u201327 September 2020, Springer. Proceedings, Part I 25."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhang, J., Hua, Y., Wang, H., Song, T., Xue, Z., Ma, R., Cao, J., and Guan, H. (2023, January 1\u20136). Gpfl: Simultaneously learning global and personalized feature information for personalized federated learning. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Paris, France.","DOI":"10.1109\/ICCV51070.2023.00465"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Liu, L., Liu, L., Shen, L., Liu, S., and Wu, B. (2023, January 1\u20136). Global Balanced Experts for Federated Long-Tailed Learning. Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), Paris, France.","DOI":"10.1109\/ICCV51070.2023.00444"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1016\/j.neucom.2021.08.141","article-title":"FedSim: Similarity guided model aggregation for Federated Learning","volume":"483","author":"Palihawadana","year":"2022","journal-title":"Neurocomputing"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1919","DOI":"10.1109\/TASLP.2019.2935803","article-title":"Using generalized Gaussian distributions to improve regression error modeling for deep learning-based speech enhancement","volume":"27","author":"Chai","year":"2019","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Chen, Z.J., Hernandez, E.E., Huang, Y.C., and Rini, S. (2022, January 16\u201320). DNN gradient lossless compression: Can GenNorm be the answer?. Proceedings of the ICC 2022-IEEE International Conference on Communications, Seoul, Republic of Korea.","DOI":"10.1109\/ICC45855.2022.9838754"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1950","DOI":"10.1109\/TIP.2025.3550013","article-title":"Generalized Gaussian Model for Learned Image Compression","volume":"34","author":"Zhang","year":"2025","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","unstructured":"Yang, H., Qiu, P., and Liu, J. (December, January 28). Taming Fat-Tailed (\u201cHeavier-Tailed\u201d with Potentially Infinite Variance) Noise in Federated Learning. Proceedings of the Advances in Neural Information Processing Systems (NeurIPS), New Orleans, LA, USA."},{"key":"ref_20","unstructured":"H\u00fcbler, F., Fatkhullin, I., and He, N. (2024). From gradient clipping to normalization for heavy tailed sgd. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, J., Chen, Z., Chong, K.F.E., Das, B., Quek, T.Q., and Yang, H.H. (2024). Robust Federated Learning Over the Air: Combating Heavy-Tailed Noise with Median Anchored Clipping. arXiv.","DOI":"10.23919\/WiOpt66569.2025.11123216"},{"key":"ref_22","first-page":"131513","article-title":"Second-order optimization under heavy-tailed noise: Hessian clipping and sample complexity limits","volume":"38","author":"Sadiev","year":"2026","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_23","unstructured":"Vukovic, M., and Jakovetic, D. (2026). Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling. arXiv."},{"key":"ref_24","unstructured":"Puchkin, N., Gorbunov, E., Kutuzov, N., and Gasnikov, A. (2024, January 2\u20134). Breaking the heavy-tailed noise barrier in stochastic optimization problems. Proceedings of the International Conference on Artificial Intelligence and Statistics, Valencia, Spain."},{"key":"ref_25","unstructured":"Bakkali, T.E., Chayti, E.M., Zhang, Q., Rahali, I., and Saadi, O. (2026). Stochastic Zeroth-Order Optimization Under Heavy-Tailed Noise. arXiv."},{"key":"ref_26","first-page":"121043","article-title":"A Near-Optimal Algorithm for Decentralized Convex-Concave Finite-Sum Minimax Optimization","volume":"38","author":"Chen","year":"2026","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"40431","DOI":"10.1109\/JIOT.2024.3456857","article-title":"Communication-Efficient Federated DNN Training: Convert, Compress, Correct","volume":"11","author":"Chen","year":"2024","journal-title":"IEEE Internet Things J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/6\/630\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:23:12Z","timestamp":1780467792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/6\/630"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,2]]},"references-count":27,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["e28060630"],"URL":"https:\/\/doi.org\/10.3390\/e28060630","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,2]]}}}