@inproceedings{22831,
  abstract     = {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.},
  author       = {Yu, Hanlin and Inal, Berfin and Arvanitidis, Georgios and Hauberg, Søren and Locatello, Francesco and Fumero, Marco},
  booktitle    = {39th Conference on Neural Information Processing Systems},
  isbn         = {9798331338275},
  issn         = {1049-5258},
  location     = {San Diego, CA, United States},
  pages        = {125316--125360},
  publisher    = {Neural Information Processing Systems Foundation},
  title        = {{Connecting neural models latent geometries with relative geodesic representations}},
  doi          = {10.52202/085713-3769},
  volume       = {38},
  year         = {2025},
}