Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators
Abstract
We study learning-theoretic foundations of operator learning, using the linear layer of the Fourier Neural Operator architecture as a model problem. First, we identify three main errors that occur during the learning process: statistical error due to finite sample size, truncation error from finite rank approximation of the operator, and discretization error from handling functional data on a finite grid of domain points. Finally, we analyze a Discrete Fourier Transform (DFT) based least squares estimator, establishing both upper and lower bounds on the aforementioned errors.
Cite
Text
Subedi and Tewari. "Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators." Transactions on Machine Learning Research, 2025.Markdown
[Subedi and Tewari. "Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators." Transactions on Machine Learning Research, 2025.](https://mlanthology.org/tmlr/2025/subedi2025tmlr-controlling/)BibTeX
@article{subedi2025tmlr-controlling,
title = {{Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators}},
author = {Subedi, Unique and Tewari, Ambuj},
journal = {Transactions on Machine Learning Research},
year = {2025},
url = {https://mlanthology.org/tmlr/2025/subedi2025tmlr-controlling/}
}