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.

翻译：学习无穷维函数空间之间的映射，即算子学习，对于许多机器学习应用至关重要。尽管基于Transformer的算子很流行，但它们通常依赖于逐token注意力。这些方法将连续场视为离散token，通常忽略了全局函数结构。我们引入了*功能注意力*，它将注意力重新解释为自适应基之间的函数对应。受几何函数映射启发，我们的方法用结构化线性算子替代了softmax亲和性。这产生了一种紧凑、可泛化、分辨率不变的表示，明确捕捉了全局依赖关系。实验表明，*功能注意力*在诸多算子学习任务中可达到最先进性能，包括求解偏微分方程、三维分割和回归，同时对不同离散化保持鲁棒性。项目页面见https://github.com/xjffff/FUNCATTN。