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We show mathematically that the model can, under certain conditions, learn reflexive, antisymmetric, and transitive relations, enabling simplified training and improved performance. Experimental results on the LETOR MSLR-WEB10K, MQ2007 and MQ2008 datasets show that the model outperforms numerous state-of-the-art methods (including a listwise approach), while being inherently simpler in structure and using a pairwise approach only.<\/jats:p>","DOI":"10.1007\/s10994-024-06644-6","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T20:28:42Z","timestamp":1741120122000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Pairwise learning to rank by neural networks revisited: reconstruction, theoretical analysis and practical performance"],"prefix":"10.1007","volume":"114","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5551-0364","authenticated-orcid":false,"given":"Marius","family":"K\u00f6ppel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Segner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Wagener","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lukas","family":"Pensel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Karwath","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stefan","family":"Kramer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,3,4]]},"reference":[{"key":"6644_CR1","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Man\u00e9, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Vi\u00e9gas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., & Zheng, X. 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