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October 15, 2025Open Access

An Approximation Theory Perspective on Machine Learning

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This review discusses the disconnect between approximation theory and machine learning, highlighting emerging trends and challenges.

Function approximation is central to machine learning, yet its theoretical foundations remain unintegrated with approximation theory.
Neural networks and kernel-based methods provide significant capabilities for function approximation, especially in challenging tasks.
The paper discusses emerging trends, including shallow/deep networks and neural operators, which are pivotal in advancing machine learning.
Understanding the gap between approximation theory and current practices is critical for improving model generalization to unseen data.

Mhaskar et al. (2025) studied this question.

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