HGA Aligns Latent Spaces Without Paired Data.

Neural networks, even when trained independently on similar data, often produce latent spaces with comparable underlying geometries, though these spaces are not directly compatible. Existing methods for aligning these latent spaces typically require "anchors" – shared sample correspondences – which can be a significant limitation. This research addresses a fundamental question: can geometric signatures alone be sufficient to recover an alignment between different latent spaces? The paper introduces HGA (Hyperspherical Gaussian Alignment), a novel method that directly optimizes a transformation between two latent spaces. Instead of relying on paired data, HGA maximizes a geometric measure of "fit" between the latent spaces themselves. This geometry-driven approach allows HGA to operate effectively in both unsupervised and weakly supervised settings. HGA has demonstrated impressive capabilities in tasks such as model stitching and recovering correspondences in multilingual word embeddings. In these applications, it manages to achieve results comparable to supervised methods, but with significantly reduced or even no need for explicit supervision. This breakthrough offers a more flexible and efficient way to integrate and leverage information across different neural network models.