Connecting neural models latent geometries with relative geodesic representations

conference paper Connecting neural models latent geometries with relative geodesic representations Advances in Neural Information Processing Systems published yes Hanlin Yu author Berfin Inal author Georgios Arvanitidis author Søren Hauberg author Francesco Locatello author 26cfd52f-2483-11ee-8040-88983bcc06d40000-0002-4850-0683 Marco Fumero author 1c1593eb-393f-11ef-bb8e-ab4f1e979650 FrLo department NeurIPS: Neural Information Processing Systems IST-BRIDGE: International postdoctoral program project 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 https://github.com/marc0git/RelativeGeodesics. Neural Information Processing Systems Foundation2025San Diego, CA, United States eng 39th Conference on Neural Information Processing Systems 1049-5258 9798331338275 2506.0159910.52202/085713-3769 38125316-125360 https://github.com/marc0git/RelativeGeodesics Yu, Hanlin, et al. “Connecting Neural Models Latent Geometries with Relative Geodesic Representations.” 39th Conference on Neural Information Processing Systems, vol. 38, Neural Information Processing Systems Foundation, 2025, pp. 125316–60, doi:<a href="https://doi.org/10.52202/085713-3769">10.52202/085713-3769</a>. H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, M. Fumero, in:, 39th Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2025, pp. 125316–125360. Yu, H., Inal, B., Arvanitidis, G., Hauberg, S., Locatello, F., & Fumero, M. (2025). Connecting neural models latent geometries with relative geodesic representations. In 39th Conference on Neural Information Processing Systems (Vol. 38, pp. 125316–125360). San Diego, CA, United States: Neural Information Processing Systems Foundation. <a href="https://doi.org/10.52202/085713-3769">https://doi.org/10.52202/085713-3769</a> Yu, Hanlin, Berfin Inal, Georgios Arvanitidis, Søren Hauberg, Francesco Locatello, and Marco Fumero. “Connecting Neural Models Latent Geometries with Relative Geodesic Representations.” In 39th Conference on Neural Information Processing Systems, 38:125316–60. Neural Information Processing Systems Foundation, 2025. <a href="https://doi.org/10.52202/085713-3769">https://doi.org/10.52202/085713-3769</a>. Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. Connecting neural models latent geometries with relative geodesic representations. In: 39th Conference on Neural Information Processing Systems. Vol 38. Neural Information Processing Systems Foundation; 2025:125316-125360. doi:<a href="https://doi.org/10.52202/085713-3769">10.52202/085713-3769</a> H. Yu, B. Inal, G. Arvanitidis, S. Hauberg, F. Locatello, and M. Fumero, “Connecting neural models latent geometries with relative geodesic representations,” in 39th Conference on Neural Information Processing Systems, San Diego, CA, United States, 2025, vol. 38, pp. 125316–125360. Yu H, Inal B, Arvanitidis G, Hauberg S, Locatello F, Fumero M. 2025. Connecting neural models latent geometries with relative geodesic representations. 39th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 38, 125316–125360. 228312026-09-06T22:02:01Z2026-09-17T07:09:28Z