Functional Attention: From Pairwise Affinities to Functional Correspondences

• URL: http://arxiv.org/abs/2605.31559v1
• Date: Fri, 29 May 2026 17:22:19 GMT
• Title: Functional Attention: From Pairwise Affinities to Functional Correspondences
• Abstract summary: We introduce emphFunctional Attention, which reinterprets attention as a functional correspondence between adaptive bases.<n>Experiments demonstrate that emphFunctional Attention can match state-of-the-art performance in many operator learning tasks.
• Score: 48.36268255718624
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Learning mappings between infinite-dimensional function spaces, or operator learning, is essential for many machine learning applications. Although transformer-based operators are popular, they often rely on token-wise attention. These methods treat continuous fields as discrete tokens and usually ignore the global functional structure. We introduce \emph{Functional Attention}, which reinterprets attention as a functional correspondence between adaptive bases. Inspired by geometric functional maps, our method replaces softmax affinities with structured linear operators. This yields a compact, generalizable, resolution-invariant representation that explicitly captures global dependencies. Experiments demonstrate that \emph{Functional Attention} can match state-of-the-art performance in many operator learning tasks, including solving PDEs, 3D segmentation, and regression, while remaining robust to varying discretizations. Project page is available at https://github.com/xjffff/FUNCATTN.

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