Variation Spaces for Encoder--Decoder Neural Operators: Approximation and Generalization
stat.ML, cs.LG, cs.NA, math.FA, math.NA, math.ST, stat.TH
Submitted: 2026-05-31
Updated: 2026-09-01
Comments: 34 pages
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures
- Towards Sharp Minimax Risk Bounds for Operator Learning
- Data Complexity Estimates for Operator Learning
- Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
- Statistical Learning Theory for Neural Operators
- Stochastic Gradient Descent for Operator Learning in Hilbert Spaces: Convergence Rates and Minimax Lower Bounds
- A Kernel-based Stochastic Approximation Framework for Nonlinear Operator Learning
- Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels
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