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The conclusion of this paper is simple: a good hierarchical hyperbolic embedding is preferred for discriminating in- and out-of-distribution samples. We introduce Balanced Hyperbolic Learning. We outline a hyperbolic class embedding algorithm that jointly optimizes for hierarchical distortion and balancing between shallow and wide subhierarchies. We then use the class embeddings as hyperbolic prototypes for classification on in-distribution data. We outline how to generalize existing out-of-distribution scoring functions to operate with hyperbolic prototypes. Empirical evaluations across 13 datasets and 13 scoring functions show that our hyperbolic embeddings outperform existing out-of-distribution approaches when trained on the same data with the same backbones. We also show that our hyperbolic embeddings outperform other hyperbolic approaches, beat state-of-the-art contrastive methods, and natively enable hierarchical out-of-distribution generalization.<\/jats:p>","DOI":"10.1007\/s11263-026-02775-6","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T02:42:46Z","timestamp":1775529766000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Balanced Hyperbolic Embeddings Are Natural Out-of-Distribution Detectors"],"prefix":"10.1007","volume":"134","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4580-9383","authenticated-orcid":false,"given":"Tejaswi","family":"Kasarla","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Max","family":"van Spengler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pascal","family":"Mettes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"key":"2775_CR1","unstructured":"Becigneul, G., Ganea, O.-E.: Riemannian adaptive optimization methods. 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In: International Joint Conference on Artificial Intelligence (2022)","DOI":"10.24963\/ijcai.2022\/517"},{"issue":"6","key":"2775_CR88","doi-asserted-by":"publisher","first-page":"1452","DOI":"10.1109\/TPAMI.2017.2723009","volume":"40","author":"B Zhou","year":"2017","unstructured":"Zhou, B., Lapedriza, A., Khosla, A., Oliva, A., & Torralba, A. (2017). Places: A 10 million image database for scene recognition. IEEE transactions on pattern analysis and machine intelligence, 40(6), 1452\u20131464.","journal-title":"IEEE transactions on pattern analysis and machine intelligence"},{"key":"2775_CR89","doi-asserted-by":"crossref","unstructured":"Zhang, Z., Xiang, X.: Decoupling maxlogit for out-of-distribution detection. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 3388\u20133397 (2023)","DOI":"10.1109\/CVPR52729.2023.00330"},{"key":"2775_CR90","unstructured":"Zhang, J., Yang, J., Wang, P., Wang, H., Lin, Y., Zhang, H., Sun, Y., Du, X., Zhou, K., Zhang, W., Li, Y., Liu, Z., Chen, Y., Hai, L.: Openood v1.5: Enhanced benchmark for out-of-distribution detection. arXiv preprint arXiv:2306.09301 (2023)"}],"container-title":["International Journal of Computer Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-026-02775-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11263-026-02775-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11263-026-02775-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T23:06:47Z","timestamp":1781824007000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11263-026-02775-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,7]]},"references-count":90,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["2775"],"URL":"https:\/\/doi.org\/10.1007\/s11263-026-02775-6","relation":{},"ISSN":["0920-5691","1573-1405"],"issn-type":[{"value":"0920-5691","type":"print"},{"value":"1573-1405","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,7]]},"assertion":[{"value":"30 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"We assume that a correct and known hierarchy is available. While it is possible to use LLM-generated hierarchies\u00a0(Liu et al.,\n                      \n                      ), verifying the correctness and usability is an exciting direction for future work. In this work, we focus on hierarchy-aware OOD generalization, i.e., structured generalization within known taxonomies, while broader domain-level generalization is beyond the current scope. The formulation of Balance Hyperbolic Learning is very well suited for discriminative tasks such as OOD detection. However, this design may limit the capacity to capture fine-grained semantic relations among nodes within the same level, particularly in tasks where intra-level similarities are context-dependent. Learning hierarchies jointly with the task, or dynamically refining them from data, remains an exciting research direction.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Limitations and Discussion"}}],"article-number":"202"}}