Minimax rates for learning spectral Barron functions by deep ReLU neural networks

arXiv:2609.39020 · stat.ML, cs.LG, cs.NA, math.NA · Submitted 2026-09-30 · Read on arXiv

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

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Activation Function — 7× in this paper · explained in 1 episode
• Curse of Dimensionality — 7× in this paper · explained in 6 episodes
• Generalization — 7× in this paper · explained in 13 episodes
• Approximation Bound — 6× in this paper · explained in 1 episode
• Sparsity — 4× in this paper · explained in 4 episodes
• Adaptivity — 1× in this paper · explained in 1 episode
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Hamming Distance — 1× in this paper · explained in 2 episodes
• Minimax Optimal Rates — 1× in this paper · explained in 2 episodes
• Neural Network Approximation — 1× in this paper · explained in 2 episodes

Sources

• Learning Sparse Compositional Functions with Norm-Constrained Neural Networks
• Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization
• The universal approximation power of finite-width deep ReLU networks
• Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networks

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