---
_id: '22831'
abstract:
- lang: eng
text: "Neural models learn representations of high-dimensional data on low-dimensional\r\nmanifolds.
Multiple factors, including stochasticities in the training process, model\r\narchitectures,
and additional inductive biases, may induce different representations,\r\neven
when learning the same task on the same data. However, it has recently been\r\nshown
that when a latent structure is shared between distinct latent spaces, relative\r\ndistances
between representations can be preserved, up to distortions. Building\r\non this
idea, we demonstrate that exploiting the differential-geometric structure of\r\nlatent
spaces of neural models, it is possible to capture precisely the transformations\r\nbetween
representational spaces trained on similar data distributions. Specifically,\r\nwe
assume that distinct neural models parametrize approximately the same underlying
manifold, and introduce a representation based on the pullback metric\r\nthat
captures the intrinsic structure of the latent space, while scaling efficiently\r\nto
large models. We validate experimentally our method on model stitching and\r\nretrieval
tasks, covering autoencoders and vision foundation discriminative models,\r\nacross
diverse architectures, datasets, pretraining schemes and modalities. Code is\r\navailable
at https://github.com/marc0git/RelativeGeodesics."
acknowledgement: "We thank Gregor Krzmanc, German Magai, Vital Fernandez for insightful
discussions in the early\r\nstages of the project. HY was supported by the Research
Council of Finland Flagship programme:\r\nFinnish Center for Artificial Intelligence
FCAI. HY wishes to acknowledge CSC - IT Center for\r\nScience, Finland, for computational
resources. GA was supported by the DFF Sapere Aude Starting\r\nGrant “GADL”. SH
was supported by a research grant (42062) from VILLUM FONDEN and partly\r\nfunded
by the Novo Nordisk Foundation through the Center for Basic Research in Life Science\r\n(NNF20OC0062606).
SH received funding from the European Research Council (ERC) under the\r\nEuropean
Union’s Horizon Programme (grant agreement 101125003). MF is supported by the MSCA\r\nIST-Bridge
fellowship which has received funding from the European Union’s Horizon 2020 research\r\nand
innovation program under the Marie Skłodowska-Curie grant agreement No 101034413."
alternative_title:
- Advances in Neural Information Processing Systems
article_processing_charge: No
arxiv: 1
author:
- first_name: Hanlin
full_name: Yu, Hanlin
last_name: Yu
- first_name: Berfin
full_name: Inal, Berfin
last_name: Inal
- first_name: Georgios
full_name: Arvanitidis, Georgios
last_name: Arvanitidis
- first_name: Søren
full_name: Hauberg, Søren
last_name: Hauberg
- first_name: Francesco
full_name: Locatello, Francesco
id: 26cfd52f-2483-11ee-8040-88983bcc06d4
last_name: Locatello
orcid: 0000-0002-4850-0683
- first_name: Marco
full_name: Fumero, Marco
id: 1c1593eb-393f-11ef-bb8e-ab4f1e979650
last_name: Fumero
citation:
ama: '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:10.52202/085713-3769'
apa: '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. https://doi.org/10.52202/085713-3769'
chicago: 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. https://doi.org/10.52202/085713-3769.
ieee: 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.
ista: '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.'
mla: 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:10.52202/085713-3769.
short: 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.
conference:
end_date: 2025-12-07
location: San Diego, CA, United States
name: 'NeurIPS: Neural Information Processing Systems'
start_date: 2025-12-02
corr_author: '1'
das_tickbox: '0'
date_created: 2026-09-06T22:02:01Z
date_published: 2025-12-01T00:00:00Z
date_updated: 2026-09-17T07:09:28Z
day: '01'
department:
- _id: FrLo
doi: 10.52202/085713-3769
ec_funded: 1
external_id:
arxiv:
- '2506.01599'
fulldoi: https://doi.org/10.52202/085713-3769
intvolume: ' 38'
language:
- iso: eng
month: '12'
oa_version: None
page: 125316-125360
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 39th Conference on Neural Information Processing Systems
publication_identifier:
eissn:
- 1049-5258
isbn:
- '9798331338275'
publication_status: published
publisher: Neural Information Processing Systems Foundation
quality_controlled: '1'
related_material:
link:
- relation: software
url: ' https://github.com/marc0git/RelativeGeodesics'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Connecting neural models latent geometries with relative geodesic representations
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 38
year: '2025'
...