Latent Functional Maps: a spectral framework for representation alignment

TL;DR

This paper introduces Latent Functional Maps, a spectral framework that aligns neural representations across different spaces, improving interpretability, comparison, and transfer of data representations in various applications.

Contribution

It presents a novel spectral geometry-based framework for comparing, aligning, and transferring neural representations, addressing challenges in modeling relations between low-dimensional manifolds.

Findings

Effective in measuring intrinsic similarity between spaces

Successful in finding correspondences in unsupervised and weakly supervised settings

Enhances downstream task performance across multiple modalities

Abstract

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.