# Unsupervised Latent Space Alignment with Hyperspherical Geodesic Matching

arXiv: https://arxiv.org/abs/2608.28840 · HTML: https://mlsanity.com/paper/2608.28840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 28 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [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)
- [Gromov-Wasserstein Alignment of Word Embedding Spaces](https://mlsanity.com/paper/1809.00013/) (2018)
- [Similarity and Matching of Neural Network Representations](https://mlsanity.com/paper/2110.14633/) (2021)
- [Generalized Linear Mode Connectivity for Transformers](https://mlsanity.com/paper/2506.22712/) (2025)

## Abstract (arXiv)

Independently trained neural networks tend to encode the same data with similar latent geometries. These latent geometries are not directly compatible, yet they can be nearly the same up to some class of transformations. While there exists many methods for alignment between different latent spaces, it is typically done using a set of shared sample correspondences, known as anchors. This leaves a fundamental question: are the geometric signatures of different latent spaces representing similar data sufficient to recover an alignment between them? To that end, we introduce HGA (Hyperspherical Gaussian Alignment), a method that directly optimizes a transformation between two latent spaces by maximizing a geometric measure of "fit" between them. Since it is driven by the geometry of the latent spaces rather than paired data, HGA can operate in both an unsupervised and weakly supervised regime. On tasks such as model stitching or multilingual word embedding correspondence recovery, HGA manages to match supervised results with minimal or no supervision.