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stat.ML2026
Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy
Baicheng Li, Haizhao Yang, Shijun Zhang
In this work, we investigate new activation functions for achieving arbitrary-accuracy Sobolev approximation by fixed-size neural networks. We first show that any function in $W^{2…
cs.LG2026
Multigrade Neural Network Approximation
Shijun Zhang, Zuowei Shen, Yuesheng Xu
We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now…