Introduces variation spaces for nonlinear operators and derives dimension-independent approximation bounds of order N^{-1/2} plus encoding errors for encoder-decoder two-layer networks, yielding algebraic rates under polynomial encoding decay.
Learning operators with stochastic gradient descent in general Hilbert spaces
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
stat.ML 2verdicts
UNVERDICTED 2representative citing papers
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.
citing papers explorer
-
Efficient Approximation for Encoder--Decoder Neural Operators via Variation Spaces
Introduces variation spaces for nonlinear operators and derives dimension-independent approximation bounds of order N^{-1/2} plus encoding errors for encoder-decoder two-layer networks, yielding algebraic rates under polynomial encoding decay.
-
Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
Establishes near-optimal dimension-independent convergence rates for regularized SGD with operator-valued kernels in statistical inverse problems for operator learning.