Approximation of Analytic Functions by ReLU Neural Networks with Adjustable Depth and Width

arXiv:2607.10589 · stat.ML, cs.IT, cs.LG, math.NA · Submitted 2026-07-12 · Read on arXiv

Yanming Lai, Defeng Sun, Yang Wang

stat.ML, cs.IT, cs.LG, math.NA

Submitted: 2026-07-12

Comments: 47 pages, 4 figures, 1 table

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• ReLU Network — 24× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Neural Network Approximation — 6× in this paper · explained in 2 episodes
• Curse of Dimensionality — 3× in this paper · explained in 6 episodes
• Generalization — 3× in this paper · explained in 14 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Expressivity — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Structural Properties — 1× in this paper · explained in 2 episodes

Sources

• Some Super-approximation Rates of ReLU Neural Networks for Korobov Functions
• Expressivity of Shallow and Deep Neural Networks for Polynomial Approximation
• Representation Benefits of Deep Feedforward Networks
• Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms
• Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks

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