{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T21:04:33Z","timestamp":1784149473968,"version":"3.55.0"},"reference-count":53,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100014761","name":"Natural Science Foundation of Qingdao","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100014761","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Shandong Province Natural Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Engineering Applications of Artificial Intelligence"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.engappai.2026.115631","type":"journal-article","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T19:11:29Z","timestamp":1784056289000},"page":"115631","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P5","title":["Dual-Space Optimization for data-free model merging"],"prefix":"10.1016","volume":"181","author":[{"given":"Hongyu","family":"Deng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengde","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Zeng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5388-9080","authenticated-orcid":false,"given":"Weifeng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.engappai.2026.115631_b1","unstructured":"Ainsworth, S., Hayase, J., Srinivasa, S., 2023. Git Re-Basin: Merging Models modulo Permutation Symmetries. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"issue":"10","key":"10.1016\/j.engappai.2026.115631_b2","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1109\/JPROC.2017.2675998","article-title":"Remote sensing image scene classification: Benchmark and state of the art","volume":"105","author":"Cheng","year":"2017","journal-title":"Proc. IEEE"},{"key":"10.1016\/j.engappai.2026.115631_b3","series-title":"Proceedings of the International Conference on Machine Learning","article-title":"Whoever started the interference should end it: Guiding data-free model merging via task vectors","author":"Cheng","year":"2025"},{"issue":"70","key":"10.1016\/j.engappai.2026.115631_b4","first-page":"1","article-title":"Scaling instruction-finetuned language models","volume":"25","author":"Chung","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.engappai.2026.115631_b5","doi-asserted-by":"crossref","unstructured":"Cimpoi, M., Maji, S., Kokkinos, I., Mohamed, S., Vedaldi, A., 2014. Describing Textures in the Wild. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition. CVPR, pp. 3606\u20133613.","DOI":"10.1109\/CVPR.2014.461"},{"issue":"3","key":"10.1016\/j.engappai.2026.115631_b6","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1038\/s42256-023-00626-4","article-title":"Parameter-efficient fine-tuning of large-scale pre-trained language models","volume":"5","author":"Ding","year":"2023","journal-title":"Nat. Mach. Intell."},{"key":"10.1016\/j.engappai.2026.115631_b7","unstructured":"Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., Houlsby, N., 2021. An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b8","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"Parameter competition balancing for model merging","author":"Du","year":"2024"},{"key":"10.1016\/j.engappai.2026.115631_b9","doi-asserted-by":"crossref","unstructured":"Gargiulo, A.A., Crisostomi, D., Bucarelli, M.S., Scardapane, S., Silvestri, F., Rodol\u00e0, E., 2024. Task Singular Vectors: Reducing Task Interference in Model Merging. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition. CVPR, pp. 18695\u201318705.","DOI":"10.1109\/CVPR52734.2025.01742"},{"issue":"3","key":"10.1016\/j.engappai.2026.115631_b10","doi-asserted-by":"crossref","first-page":"A1139","DOI":"10.1137\/130938700","article-title":"Subspace iteration randomization and singular value problems","volume":"37","author":"Gu","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.engappai.2026.115631_b11","article-title":"Localize-and-stitch: Efficient model merging via sparse task arithmetic","author":"He","year":"2025","journal-title":"Trans. Mach. Learn. Res."},{"key":"10.1016\/j.engappai.2026.115631_b12","doi-asserted-by":"crossref","DOI":"10.1109\/JSTARS.2019.2918242","article-title":"EuroSAT: A novel dataset and deep learning benchmark for land use and land cover classification","author":"Helber","year":"2019","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote. Sens."},{"key":"10.1016\/j.engappai.2026.115631_b13","unstructured":"Hu, E.J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., Chen, W., 2022. LoRA: Low-Rank Adaptation of Large Language Models. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b14","unstructured":"Ilharco, G., Ribeiro, M.T., Wortsman, M., Schmidt, L., Hajishirzi, H., Farhadi, A., 2023. Editing models with task arithmetic. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b15","unstructured":"Jin, X., Ren, X., Preotiuc-Pietro, D., Cheng, P., 2023. Dataless Knowledge Fusion by Merging Weights of Language Models. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b16","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.111691","article-title":"EigenGAN: An SVD subspace-based learning for image generation using conditional GAN","volume":"293","author":"Kas","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"10.1016\/j.engappai.2026.115631_b17","unstructured":"Kim, H., Papamakarios, G., Mnih, A., 2021. The lipschitz constant of self-attention. In: Proceedings of the International Conference on Machine Learning. ICML, pp. 5562\u20135571."},{"key":"10.1016\/j.engappai.2026.115631_b18","series-title":"Proceedings of the IEEE International Conference on Computer Vision Workshops","first-page":"554","article-title":"3D object representations for fine-grained categorization","author":"Krause","year":"2013"},{"issue":"11","key":"10.1016\/j.engappai.2026.115631_b19","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"LeCun","year":"1998","journal-title":"Proc. IEEE"},{"key":"10.1016\/j.engappai.2026.115631_b20","series-title":"Branch-train-merge: Embarrassingly parallel training of expert language models","author":"Li","year":"2023"},{"issue":"1","key":"10.1016\/j.engappai.2026.115631_b21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s11263-024-02181-w","article-title":"A comprehensive survey on test-time adaptation under distribution shifts","volume":"133","author":"Liang","year":"2025","journal-title":"Int. J. Comput. Vis."},{"key":"10.1016\/j.engappai.2026.115631_b22","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2025.113298","article-title":"BEFM: A balanced and efficient fine-tuning model in class-incremental learning","volume":"315","author":"Liu","year":"2025","journal-title":"Knowl.-Based Syst."},{"issue":"9","key":"10.1016\/j.engappai.2026.115631_b23","doi-asserted-by":"crossref","DOI":"10.1145\/3560815","article-title":"Pre-train, prompt, and predict: A systematic survey of prompting methods in natural language processing","volume":"55","author":"Liu","year":"2023","journal-title":"ACM Comput. Surv."},{"key":"10.1016\/j.engappai.2026.115631_b24","unstructured":"Marczak, D., Magistri, S., Cygert, S., Twardowski, B., Bagdanov, A.D., van de Weijer, J., 2025. No Task Left Behind: Isotropic Model Merging with Common and Task-Specific Subspaces. In: Proceedings of the International Conference on Machine Learning. ICML."},{"key":"10.1016\/j.engappai.2026.115631_b25","first-page":"17703","article-title":"Merging models with fisher-weighted averaging","volume":"vol. 35","author":"Matena","year":"2022"},{"key":"10.1016\/j.engappai.2026.115631_b26","first-page":"4","article-title":"Reading digits in natural images with unsupervised feature learning","volume":"vol. 2011","author":"Netzer","year":"2011"},{"key":"10.1016\/j.engappai.2026.115631_b27","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"Task arithmetic in the tangent space: improved editing of pre-trained models","author":"Ortiz-Jimenez","year":"2023"},{"key":"10.1016\/j.engappai.2026.115631_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.knosys.2024.112415","article-title":"MTLSC-Diff: Multitask learning with diffusion models for hyperspectral image super-resolution and classification","volume":"303","author":"Qu","year":"2024","journal-title":"Knowl.-Based Syst."},{"key":"10.1016\/j.engappai.2026.115631_b29","unstructured":"Radford, A., Kim, J.W., Hallacy, C., Ramesh, A., Goh, G., Agarwal, S., Sastry, G., Askell, A., Mishkin, P., Clark, J., 2021. Learning transferable visual models from natural language supervision. In: Proceedings of the International Conference on Machine Learning. ICML, pp. 8748\u20138763."},{"key":"10.1016\/j.engappai.2026.115631_b30","doi-asserted-by":"crossref","unstructured":"Saha, G., Roy, K., 2023. Continual learning with scaled gradient projection. In: Proceedings of the AAAI Conference on Artificial Intelligence. AAAI.","DOI":"10.1609\/aaai.v37i8.26157"},{"key":"10.1016\/j.engappai.2026.115631_b31","doi-asserted-by":"crossref","unstructured":"Shen, G., Zhang, S., Chen, X., Deng, Z.-H., 2021. Generative Feature Replay with Orthogonal Weight Modification for Continual Learning. In: Proceedings of the International Joint Conference on Neural Networks. IJCNN, pp. 1\u20138.","DOI":"10.1109\/IJCNN52387.2021.9534437"},{"key":"10.1016\/j.engappai.2026.115631_b32","doi-asserted-by":"crossref","unstructured":"Stallkamp, J., Schlipsing, M., Salmen, J., Igel, C., 2011. The German Traffic Sign Recognition Benchmark: A multi-class classification competition. In: Proceedings of the International Joint Conference on Neural Networks. IJCNN, pp. 1453\u20131460.","DOI":"10.1109\/IJCNN.2011.6033395"},{"key":"10.1016\/j.engappai.2026.115631_b33","unstructured":"Stoica, G., Bolya, D., Bjorner, J.B., Ramesh, P., Hearn, T., Hoffman, J., 2024. ZipIt! Merging Models from Different Tasks without Training. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b34","unstructured":"Stoica, G., Ramesh, P., Ecsedi, B., Choshen, L., Hoffman, J., 2025. Model merging with SVD to tie the Knots. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b35","article-title":"Merging by matching models in task parameter subspaces","author":"Tam","year":"2024","journal-title":"Trans. Mach. Learn. Res."},{"key":"10.1016\/j.engappai.2026.115631_b36","series-title":"Concrete subspace learning based interference elimination for multi-task model fusion","author":"Tang","year":"2023"},{"key":"10.1016\/j.engappai.2026.115631_b37","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"Merging on the fly without retraining: A sequential approach to scalable continual model merging","author":"Tang","year":"2025"},{"key":"10.1016\/j.engappai.2026.115631_b38","series-title":"Llama: Open and efficient foundation language models","author":"Touvron","year":"2023"},{"issue":"7","key":"10.1016\/j.engappai.2026.115631_b39","first-page":"3614","article-title":"Multi-task learning for dense prediction tasks: A survey","volume":"44","author":"Vandenhende","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Machine Intell."},{"key":"10.1016\/j.engappai.2026.115631_b40","unstructured":"Wang, K., Dimitriadis, N., Ortiz-Jim\u00e9nez, G., Fleuret, F., Frossard, P., 2024. Localizing task information for improved model merging and compression. In: Proceedings of the International Conference on Machine Learning. ICML."},{"key":"10.1016\/j.engappai.2026.115631_b41","doi-asserted-by":"crossref","unstructured":"Wang, A., Singh, A., Michael, J., Hill, F., Levy, O., Bowman, S.R., 2019. GLUE: A multi-task benchmark and analysis platform for natural language understanding. In: Proceedings of the International Conference on Learning Representations. ICLR.","DOI":"10.18653\/v1\/W18-5446"},{"key":"10.1016\/j.engappai.2026.115631_b42","unstructured":"Wei, Y., Tang, A., Shen, L., Hu, Z., Yuan, C., Cao, X., 2025. Modeling Multi-Task Model Merging as Adaptive Projective Gradient Descent. In: Proceedings of the International Conference on Machine Learning. ICML."},{"key":"10.1016\/j.engappai.2026.115631_b43","unstructured":"Wortsman, M., Ilharco, G., Gadre, S.Y., Roelofs, R., Gontijo-Lopes, R., Morcos, A.S., Namkoong, H., Farhadi, A., Carmon, Y., Kornblith, S., Schmidt, L., 2022. Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time. In: Proceedings of the International Conference on Machine Learning. ICML, pp. 23965\u201323998."},{"key":"10.1016\/j.engappai.2026.115631_b44","doi-asserted-by":"crossref","DOI":"10.1007\/s11263-014-0748-y","article-title":"SUN database: Exploring a large collection of scene categories","author":"Xiao","year":"2016","journal-title":"Int. J. Comput. Vis."},{"key":"10.1016\/j.engappai.2026.115631_b45","series-title":"Multi-task model merging via adaptive weight disentanglement","author":"Xiong","year":"2025"},{"key":"10.1016\/j.engappai.2026.115631_b46","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"TIES-merging: Resolving interference when merging models","author":"Yadav","year":"2023"},{"key":"10.1016\/j.engappai.2026.115631_b47","series-title":"Model merging in LLMs, MLLMs, and beyond: Methods, theories, applications and opportunities","author":"Yang","year":"2024"},{"key":"10.1016\/j.engappai.2026.115631_b48","unstructured":"Yang, E., Shen, L., Wang, Z., Guo, G., Chen, X., Wang, X., Tao, D., 2024b. Representation surgery for multi-task model merging. In: Proceedings of the International Conference on Machine Learning. ICML, pp. 2325\u20132349."},{"key":"10.1016\/j.engappai.2026.115631_b49","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"Continual model merging without data: Dual projections for balancing stability and plasticity","author":"Yang","year":"2025"},{"key":"10.1016\/j.engappai.2026.115631_b50","unstructured":"Yang, E., Wang, Z., Shen, L., Liu, S., Guo, G., Wang, X., Tao, D., 2024c. AdaMerging: Adaptive Model Merging for Multi-Task Learning. In: Proceedings of the International Conference on Learning Representations. ICLR."},{"key":"10.1016\/j.engappai.2026.115631_b51","unstructured":"Yu, L., Yu, B., Yu, H., Huang, F., Li, Y., 2024. Language models are super mario: absorbing abilities from homologous models as a free lunch. In: Proceedings of the International Conference on Machine Learning. ICML."},{"key":"10.1016\/j.engappai.2026.115631_b52","series-title":"Advances in Neural Information Processing Systems (NeurIPS)","article-title":"Composing parameter-efficient modules with arithmetic operations","author":"Zhang","year":"2023"},{"key":"10.1016\/j.engappai.2026.115631_b53","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Song, L., Wang, B., Chen, W., 2024. MetaGPT: Merging Large Language Models Using Model Exclusive Task Arithmetic. In: Proceedings of the Conference on Empirical Methods in Natural Language Processing. EMNLP.","DOI":"10.18653\/v1\/2024.emnlp-main.102"}],"container-title":["Engineering Applications of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626019159?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0952197626019159?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T20:06:54Z","timestamp":1784146014000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0952197626019159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":53,"alternative-id":["S0952197626019159"],"URL":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115631","relation":{},"ISSN":["0952-1976"],"issn-type":[{"value":"0952-1976","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Dual-Space Optimization for data-free model merging","name":"articletitle","label":"Article Title"},{"value":"Engineering Applications of Artificial Intelligence","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.engappai.2026.115631","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115631"}}