{"external_id":{"arxiv":["2506.01599"]},"alternative_title":["Advances in Neural Information Processing Systems"],"ec_funded":1,"has_accepted_license":"1","year":"2025","oa_version":"Published Version","publisher":"Neural Information Processing Systems Foundation","corr_author":"1","day":"15","author":[{"first_name":"Hanlin","last_name":"Yu","full_name":"Yu, Hanlin"},{"last_name":"Inal","first_name":"Befrin","full_name":"Inal, Befrin"},{"first_name":"Georgios","last_name":"Arvanitidis","full_name":"Arvanitidis, Georgios"},{"full_name":"Hauberg, Soren","last_name":"Hauberg","first_name":"Soren"},{"full_name":"Locatello, Francesco","orcid":"0000-0002-4850-0683","id":"26cfd52f-2483-11ee-8040-88983bcc06d4","first_name":"Francesco","last_name":"Locatello"},{"last_name":"Fumero","first_name":"Marco","id":"1c1593eb-393f-11ef-bb8e-ab4f1e979650","full_name":"Fumero, Marco"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        38","article_processing_charge":"No","type":"conference","publication":"39th Annual Conference on Neural Information Processing Systems","date_updated":"2026-02-11T09:03:37Z","department":[{"_id":"FrLo"}],"volume":38,"conference":{"name":"NeurIPS: Neural Information Processing Systems","end_date":"2025-12-07","location":"San Diego, CA, United States","start_date":"2025-12-02"},"date_created":"2026-01-29T14:31:52Z","publication_identifier":{"issn":["1049-5258"]},"publication_status":"epub_ahead","status":"public","file_date_updated":"2026-01-29T14:31:42Z","date_published":"2025-12-15T00:00:00Z","acknowledgement":"We thank Gregor Krzmanc, German Magai, Vital Fernandez for insightful discussions in the early stages of the project. HY was supported by the Research Council of Finland Flagship programme: Finnish Center for Artificial Intelligence FCAI. HY wishes to acknowledge CSC - IT Center for Science, Finland, for computational resources. GA was supported by the DFF Sapere Aude Starting Grant “GADL”. SH was supported by a research grant (42062) from VILLUM FONDEN and partly funded by the Novo Nordisk Foundation through the Center for Basic Research in Life Science (NNF20OC0062606). SH received funding from the European Research Council (ERC) under the European Union’s Horizon Programme (grant agreement 101125003). MF is supported by the MSCA IST-Bridge fellowship which has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 101034413.","quality_controlled":"1","abstract":[{"lang":"eng","text":"Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different representations, even when learning the same task on the same data. However, it has recently been shown that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions. Building on this idea, we demonstrate that exploiting the differential-geometric structure of latent spaces of neural models, it is possible to capture precisely the transformations between representational spaces trained on similar data distributions. Specifically, we assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric that captures the intrinsic structure of the latent space, while scaling efficiently to large models. We validate experimentally our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models, across diverse architectures, datasets, pretraining schemes and modalities. Code is available at the following link."}],"OA_type":"gold","OA_place":"publisher","title":"Connecting neural models latent geometries with relative geodesic representations","month":"12","language":[{"iso":"eng"}],"oa":1,"ddc":["000"],"arxiv":1,"_id":"21074","citation":{"ama":"Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. Connecting neural models latent geometries with relative geodesic representations. In: <i>39th Annual Conference on Neural Information Processing Systems</i>. Vol 38. Neural Information Processing Systems Foundation; 2025.","chicago":"Yu, Hanlin, Befrin Inal, Georgios Arvanitidis, Soren Hauberg, Francesco Locatello, and Marco Fumero. “Connecting Neural Models Latent Geometries with Relative Geodesic Representations.” In <i>39th Annual Conference on Neural Information Processing Systems</i>, Vol. 38. Neural Information Processing Systems Foundation, 2025.","short":"H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, M. Fumero, in:, 39th Annual Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2025.","mla":"Yu, Hanlin, et al. “Connecting Neural Models Latent Geometries with Relative Geodesic Representations.” <i>39th Annual Conference on Neural Information Processing Systems</i>, vol. 38, Neural Information Processing Systems Foundation, 2025.","apa":"Yu, H., Inal, B., Arvanitidis, G., Hauberg, S., Locatello, F., &#38; Fumero, M. (2025). Connecting neural models latent geometries with relative geodesic representations. In <i>39th Annual Conference on Neural Information Processing Systems</i> (Vol. 38). San Diego, CA, United States: Neural Information Processing Systems Foundation.","ieee":"H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, and M. Fumero, “Connecting neural models latent geometries with relative geodesic representations,” in <i>39th Annual Conference on Neural Information Processing Systems</i>, San Diego, CA, United States, 2025, vol. 38.","ista":"Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. 2025. Connecting neural models latent geometries with relative geodesic representations. 39th Annual Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 38."},"file":[{"checksum":"b1a645418025f46394764cd16d0cb089","relation":"main_file","file_size":7749349,"date_updated":"2026-01-29T14:31:42Z","file_id":"21075","date_created":"2026-01-29T14:31:42Z","content_type":"application/pdf","creator":"flocatel","access_level":"open_access","success":1,"file_name":"2506.01599v2.pdf"}],"project":[{"name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}}