Latent Functional Maps: a spectral framework for representation alignment
This provides a versatile tool for the representation learning community to align and transfer representations, though it appears incremental as it builds on existing spectral methods.
The paper tackles the challenge of modeling relationships between low-dimensional manifolds in neural representations by integrating spectral geometry principles, resulting in a framework that improves interpretability and performance on downstream tasks like stitching and retrieval across multiple modalities.
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.