Resolution-Independent Analysis of Encoder--Decoder Operator Learning via Limiting Kernels
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 independently of the encoding resolution. For regularized stochastic gradient descent, we establis...
| Authors | Lei Shi, Jia-Qi Yang, Ding-Xuan Zhou |
|---|---|
| Primary category | stat.ML |
| Published | 12 September 2026 |
| Last updated at source | 12 September 2026 |
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