Relative representations are an established approach to zero-shot model stitching, consisting of a non-trainable transformation of the latent space of a deep neural network. Based on insights of topological and geometric nature, we propose two improvements to relative representations. First, we introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations. The latter coincides with the symmetries in parameter space induced by common activation functions. Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes. We provide an empirical investigation on a natural language task, where both the proposed variations yield improved performance on zero-shot model stitching.
View on arXiv@article{garcía-castellanos2025_2409.10967,
title={ Relative Representations: Topological and Geometric Perspectives },
author={ Alejandro García-Castellanos and Giovanni Luca Marchetti and Danica Kragic and Martina Scolamiero },
journal={arXiv preprint arXiv:2409.10967},
year={ 2025 }
}