论文标题
通过分段性化激活的深神经网络同时近似平滑函数及其导数
Simultaneous approximation of a smooth function and its derivatives by deep neural networks with piecewise-polynomial activations
论文作者
论文摘要
本文研究了具有分段多项式激活功能的深神经网络的近似特性。我们得出了深神经网络所需的深度，宽度和稀疏性，以将任何Hölder平滑功能近似于HölderNorms中给定的近似误差，以使该神经网络的所有权重均受$ 1 $的限制。后一个功能对于控制许多统计和机器学习应用中的概括错误至关重要。
This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any Hölder smooth function up to a given approximation error in Hölder norms in such a way that all weights of this neural network are bounded by $1$. The latter feature is essential to control generalization errors in many statistical and machine learning applications.
