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This paper presents principled approaches for converting popular neural network architectures (CNNs, GNNs, transformers) into neural operators that learn mappings between infinite-dimensional function spaces, enabling consistent predictions across different discretizations for scientific modeling. Published in Nature Machine Intelligence.
Functional Attention is a novel attention mechanism that reinterprets attention as a functional correspondence between adaptive bases, replacing softmax affinities with structured linear operators inspired by geometric functional maps. The method achieves state-of-the-art performance on operator learning tasks including PDE solving and 3D segmentation while remaining resolution-invariant.