# 函数注意力：从成对亲和性到函数对应

- 来源：HuggingFace Daily Papers（社区热门论文）
- 发布时间：2026-05-29 08:00
- AIHOT 分数：50
- AIHOT 链接：https://aihot.virxact.com/items/cmpzo0eqk05bgslkpzg9nmjs7
- 原文链接：https://arxiv.org/abs/2605.31559

## AI 摘要

Functional Attention 将注意力机制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，用结构化线性算子替代 softmax 亲和性，从而得到紧凑、可泛化且分辨率不变的表示，显式捕捉全局依赖。实验表明，该方法在求解 PDE、3D 分割和回归等算子学习任务中达到 SOTA 性能，并对不同离散化保持鲁棒。

## 正文

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 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 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.