证明了神经网络在弱紧测度族下的分布鲁棒逼近性。
Distributionally robust approximation property of neural networks
- 在Orlicz空间中证明神经网络的稠密性，突破传统L^p框架。
- 涵盖前馈、深窄网络与函数输入等多种主流架构。
- 为复杂分布场景下的模型泛化提供理论支持，适合理论研究者。
本文建立了几类神经网络在弱紧测度族上的一致通用逼近性质。为此，证明了这些神经网络在Orlicz空间中稠密，从而将经典通用逼近定理推广至传统的L^p框架之外。所涵盖的神经网络类别包括广泛使用的前馈网络（非多项式激活函数）、具有ReLU激活函数的深窄网络以及函数输入神经网络。
原文摘要 · Abstract (English)
The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond the traditional $L^p$-setting. The covered classes of neural networks include widely used architectures like feedforward neural networks with non-polynomial activation functions, deep narrow networks with ReLU activation functions and functional input neural networks.
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