# Connecting Neural Models Latent Geometries with Relative Geodesic Representations

arXiv: https://arxiv.org/abs/2506.01599 · HTML: https://mlsanity.com/paper/2506.01599/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 73 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Revisiting Model Stitching to Compare Neural Representations](https://mlsanity.com/paper/2106.07682/) (2021)
- [Relative representations enable zero-shot latent space communication](https://mlsanity.com/paper/2209.15430/) (2022)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Linearly Mapping from Image to Text Space](https://mlsanity.com/paper/2209.15162/) (2022)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [On Linear Identifiability of Learned Representations](https://mlsanity.com/paper/2007.00810/) (2020)
- [The Geometry of Multilingual Language Model Representations](https://mlsanity.com/paper/2205.10964/) (2022)
- [Neural Collapse: A Review on Modelling Principles and Generalization](https://mlsanity.com/paper/2206.04041/) (2022)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Similarity and Matching of Neural Network Representations](https://mlsanity.com/paper/2110.14633/) (2021)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Text-To-Concept (and Back) via Cross-Model Alignment](https://mlsanity.com/paper/2305.06386/) (2023)
- [Can Neural Nets Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspective](https://mlsanity.com/paper/2203.08124/) (2022)
- [Latent Space Translation via Semantic Alignment](https://mlsanity.com/paper/2311.00664/) (2023)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [ASIF: Coupled Data Turns Unimodal Models to Multimodal Without Training](https://mlsanity.com/paper/2210.01738/) (2022)

## Built on by (most cited first, 4 of 4)

- [The Information Geometry of Softmax: Probing and Steering](https://mlsanity.com/paper/2602.15293/) (2026)
- [Cross-Model Semantics in Representation Learning](https://mlsanity.com/paper/2508.03649/) (2025)
- [A Theory of Speciation in Generative Diffusion Models on Compact Riemannian Manifolds](https://mlsanity.com/paper/2608.23798/) (2026)
- [A Stitch in Time Saves Nine: Preserving Policy Compatibility Under Perception Updates in End-to-End Autonomous Driving](https://mlsanity.com/paper/2606.21509/) (2026)

## Abstract (arXiv)

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.