Connecting Neural Models Latent Geometries with Relative Geodesic Representations

Fuente: arXiv
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Main Authors: Yu, Hanlin, Inal, Berfin, Arvanitidis, Georgios, Hauberg, Soren, Locatello, Francesco, Fumero, Marco
Format: Preprint
Published: 2025
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author Yu, Hanlin
Inal, Berfin
Arvanitidis, Georgios
Hauberg, Soren
Locatello, Francesco
Fumero, Marco
author_facet Yu, Hanlin
Inal, Berfin
Arvanitidis, Georgios
Hauberg, Soren
Locatello, Francesco
Fumero, Marco
contents 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, and pretraining schemes.
format Preprint
id arxiv_https___arxiv_org_abs_2506_01599
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Connecting Neural Models Latent Geometries with Relative Geodesic Representations
Yu, Hanlin
Inal, Berfin
Arvanitidis, Georgios
Hauberg, Soren
Locatello, Francesco
Fumero, Marco
Machine Learning
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, and pretraining schemes.
title Connecting Neural Models Latent Geometries with Relative Geodesic Representations
topic Machine Learning
url https://arxiv.org/abs/2506.01599