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, demonstrating that latent functional
maps can serve as a swiss-army knife for representation alignment.

将光谱几何原理融入神经建模中，提出一个多功能框架，通过在功能域中比较不同空间，测量其内在相似性，找到它们之间的对应关系，并有效地在不同空间之间转移表示，从而在各种应用中验证了我们的框架，展示了潜在的功能映射可以作为表示对齐的多功能工具。