Error Bounds for Learning Fourier Linear Operators

Autor:	Subedi, Unique, Tewari, Ambuj
Rok vydání:	2024
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We investigate the problem of learning operators between function spaces, focusing on the linear layer of the Fourier Neural Operator. 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. Comment: 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.09004 Zobrazit plný text záznamu View this record from Arxiv