English(EN) Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

新的激活函数使固定大小神经网络实现任意精度

作者 PulseAugur 编辑部 · [2 个来源] · 2026-06-15 17:12

研究人员引入了新的激活函数，即基本通用激活函数（EUAF）和可微通用激活函数（DUAF），旨在使固定大小的神经网络能够实现任意精度的Sobolev近似。研究表明，使用这些新型激活函数的网络可以以任意精度在$W^{s-1, ext{inf}}$-范数下逼近$W^{s, ext{inf}}((a,b)^d)$内的函数。文章提供了网络宽度和深度的显式界限，并探讨了DUAF的S型变体。 AI

影响引入了可能增强固定大小神经网络逼近能力的新型激活函数。

排序理由该集群包含一篇详细介绍神经网络激活函数新理论贡献的学术论文。

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报道来源 [2]

arXiv cs.LG TIER_1 English(EN) · Baicheng Li, Haizhao Yang, Shijun Zhang · 2026-06-16 04:00

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

arXiv:2606.16975v1 Announce Type: cross Abstract: 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 $W^{2,\infty}((a,b)^d)$ can be approximated with arbitr…
arXiv stat.ML TIER_1 English(EN) · Shijun Zhang · 2026-06-15 17:12

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

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 $W^{2,\infty}((a,b)^d)$ can be approximated with arbitrary accuracy, measured in the $W^{1,\infty}$-norm,…

报道来源 [2]

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

Sobolev Approximation by Fixed-Size Neural Networks with Arbitrary Accuracy

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