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An approximation theory perspective on machine learning
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DOI：10.1016/j.neunet.2026.108841.png)
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Abstract
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• This review bridges gaps between approximation theory and machine learning. • Introduces manifold-free function approximation using local kernels and wavelet-like expansions. • Analyzes expressivity of deep vs. shallow networks with emphasis on compositional design. • Examines error estimates for neural operators and physics-informed neural surrogates. • Proposes new perspectives like classification as signal separation and outlines key open questions.
Keywords:
Approximation theory
Machine learning
Local kernels
Neural operators
Physics informed neural surrogates
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