Variation Spaces for Encoder--Decoder Neural Operators: Approximation and Generalization
A variation space for nonlinear operators between Hilbert spaces, defined through vector-valued Borel measures of bounded variation, is formulated and analyzed, which yields algebraic approximation and learning rates in contrast to the complexity barriers for Lipschitz and Fr\'echet differentiable operator classes.
Jia-Qi Yang, Lei Shi
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