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Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels

arXiv · AI, language, vision and robotics · article · Sep 12, 2026 · UTC

Operator learning is formulated on function spaces, but training data are typically available only through finite-dimensional representations. In encoder--decoder architectures, a matrix-valued kernel on the encoded space induces an operator-valued kernel on the original function spaces, and the corresponding reproducing kernel Hilbert spaces are isometrically isomorphic. As the input and output resolutions increase, the induced kernels converge to a limiting kernel, in the sense of operator-norm convergence of their associated integral operators, allowing regularity assumptions to be stated i

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