Latent functional maps: A spectral framework for representation alignment

conference paper Latent functional maps: A spectral framework for representation alignment Advances in Neural Information Processing Systems published yes Marco Fumero author 1c1593eb-393f-11ef-bb8e-ab4f1e979650 Marco Pegoraro author Valentino Maiorca author Francesco Locatello author 26cfd52f-2483-11ee-8040-88983bcc06d40000-0002-4850-0683 Emanuele Rodolà author FrLo department NeurIPS: Neural Information Processing Systems IST-BRIDGE: International postdoctoral program project 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 Neural Information Processing Systems Foundation2024Vancouver, Canada eng 38th Conference on Neural Information Processing Systems 1049-5258 2406.14183 37 Fumero, Marco, Marco Pegoraro, Valentino Maiorca, Francesco Locatello, and Emanuele Rodolà. “Latent Functional Maps: A Spectral Framework for Representation Alignment.” In 38th Conference on Neural Information Processing Systems, Vol. 37. Neural Information Processing Systems Foundation, 2024. Fumero M, Pegoraro M, Maiorca V, Locatello F, Rodolà E. Latent functional maps: A spectral framework for representation alignment. In: 38th Conference on Neural Information Processing Systems. Vol 37. Neural Information Processing Systems Foundation; 2024. Fumero, M., Pegoraro, M., Maiorca, V., Locatello, F., & Rodolà, E. (2024). Latent functional maps: A spectral framework for representation alignment. In 38th Conference on Neural Information Processing Systems (Vol. 37). Vancouver, Canada: Neural Information Processing Systems Foundation. Fumero M, Pegoraro M, Maiorca V, Locatello F, Rodolà E. 2024. Latent functional maps: A spectral framework for representation alignment. 38th Conference on Neural Information Processing Systems. NeurIPS: Neural Information Processing Systems, Advances in Neural Information Processing Systems, vol. 37. Fumero, Marco, et al. “Latent Functional Maps: A Spectral Framework for Representation Alignment.” 38th Conference on Neural Information Processing Systems, vol. 37, Neural Information Processing Systems Foundation, 2024. M. Fumero, M. Pegoraro, V. Maiorca, F. Locatello, E. Rodolà, in:, 38th Conference on Neural Information Processing Systems, Neural Information Processing Systems Foundation, 2024. M. Fumero, M. Pegoraro, V. Maiorca, F. Locatello, and E. Rodolà, “Latent functional maps: A spectral framework for representation alignment,” in 38th Conference on Neural Information Processing Systems, Vancouver, Canada, 2024, vol. 37. 195152025-04-06T22:01:32Z2025-05-14T11:36:51Z