Unsupervised Latent Space Alignment with Hyperspherical Geodesic Matching

Researchers introduced HGA (Hyperspherical Gaussian Alignment), a method that aligns latent spaces of independently trained neural networks by maximizing a geometric fit, eliminating the need for paired anchors. On tasks like model stitching and multilingual word embedding correspondence recovery, HGA matches supervised results with minimal or no supervision.

arXiv:2608.28840v1 Announce Type: new Abstract: 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.