Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

arXiv:2606.16975 · stat.ML, cs.LG · Submitted 2026-06-15 · Read on arXiv

Baicheng Li, Haizhao Yang, Shijun Zhang

stat.ML, cs.LG

Submitted: 2026-06-15

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

Terminology

• Accuracy — 31× in this paper · explained in 1 episode
• Activation Function — 29× in this paper · explained in 1 episode
• Elementary Universal Activation Function — 5× in this paper
• Neural Network Approximation — 3× in this paper · explained in 2 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Approximation Bound — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• PDE residual — 1× in this paper · explained in 2 episodes

Sources

• Mathematical theory of deep learning

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