@inproceedings{
fumero2024latent,
title={Latent Functional Maps: a spectral framework for representation alignment},
author={Marco Fumero and Marco Pegoraro and Valentino Maiorca and Francesco Locatello and Emanuele Rodol{\`a}},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=mfvKEdJ4zW}
}
Neural models learn data representations that lie on low-dimensional manifolds, yet modeling the relation between these representational spaces is an ongoing challenge.
By integrating spectral geometry principles into neural modeling, we show that this problem can be better addressed in the functional domain, mitigating complexity, while enhancing interpretability and performances on downstream tasks. 
To this end, we introduce a multi-purpose framework to the representation learning community, which allows to: (i) compare different spaces in an interpretable way and measure their intrinsic similarity; (ii) find correspondences between them, both in unsupervised and weakly supervised settings, and (iii) to effectively transfer representations between distinct spaces.
We validate our framework on various applications, ranging from stitching to retrieval tasks, and on multiple modalities, demonstrating that Latent Functional Maps can serve as a swiss-army knife for representation alignment.
Latent Functional Maps: a spectral framework for representation alignment
Marco Fumero Marco Pegoraro Valentino Maiorca Francesco Locatello Emanuele Rodolà