Function graph transformers universally approximate operators between function spaces
We study the approximation of nonlinear operators between function spaces by transformers. Our approach is to lift functions to measures supported on their graphs and leverage a recently introduced measure-theoretic view of transformers. A function $h$ is represented by its graph measure $γ_h$, with finite tokens $\{(x_j,h(x_j))\}_{j=1}^N$ being its empirical approximations. We show that this framework elegantly models discretization refinement via convergence of measures and provides a natural setting for operator learning. Within this framework, we introduce function graph transformers, a graph-preserving subclass of measure-theoretic transformers that maps graph measures to graph measu...
| Authors | Takashi Furuya, David Mis, Ivan Dokmanić et al. |
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| Primary category | cs.LG |
| Published | 18 May 2026 |
| Last updated at source | 18 May 2026 |
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