Functional Attention

Functional Attention: Reinterpreting Attention as Functional Correspondences for Operator Learning

This paper introduces Functional Attention, a novel attention mechanism for operator learning that replaces standard softmax token-wise affinities with structured linear operators inspired by geometric functional maps. The approach treats attention as a correspondence between adaptive bases rather than discrete tokens, yielding a resolution-invariant, globally-aware representation. Experiments show competitive or state-of-the-art performance on PDE solving, 3D segmentation, and regression tasks, with robustness to varying discretizations.