Latent functional maps

Marco Fumero, Marco Pegoraro, Valentino Maiorca, Francesco Locatello, Emanuele Rodolà

Track: Extended abstract

Keywords: Representation alignment; Spectral methods

TL;DR: Latent functional maps (LFM) model relationships between latent spaces using spectral geometry. LFM provides a robust framework for comparing and transferring information in both unsupervised and weakly supervised settings.

Abstract: Neural models learn data representations which lie on low dimensional manifolds, yet modelling 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, demonstrating that latent functional maps can serve as swiss army knife for representation alignment.

Submission Number: 7