Error bounds in Sobolev norms for approximations with norm constrained ReLU neural networks

arXiv:2609.19937 · stat.ML, cs.LG · Submitted 2026-09-17 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-17

Updated: 2026-09-17

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

Terminology

• Approximation Bound — 5× in this paper · explained in 1 episode
• Adam — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Adversarial Examples — 2× in this paper · explained in 2 episodes
• Regularization — 2× in this paper · explained in 3 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Sample Complexity — 2× in this paper · explained in 15 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Elias — 1× in this paper · explained in 2 episodes
• Hilbert Space — 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
• Approximation bounds for norm constrained deep neural networks
• Nearly Optimal Approximation Rates for Deep Super ReLU Networks on Sobolev Spaces

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