Work

Dimension-independent learning rates for high-dimensional classification problems

Year: 2025

Type: article

Abstract: In this paper, we study the problem of approximating and estimating classification functions that have their decision boundary in the [Formula: see text] space. Functions of [Formula: see text] type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every [Formula: see text] function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. We leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries.

Source: Analysis and Applications

DOI: 10.1142/s0219530525500496

Authors: Andres Felipe Lerma-Pineda, Philipp Petersen, Simon Frieder, Thomas Lukasiewicz

Institutions: University of Vienna, University of Oxford, TU Wien

Language: English

Topic: Neural Networks and Applications

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: AXA Research Fund, Austrian Science Fund

Award: Structured Singularities in Deep Learning