论文标题
在可变lebesgue空间中与神经网络的近似
Approximation with Neural Networks in Variable Lebesgue Spaces
论文作者
论文摘要
本文涉及可变lebesgue空间中神经网络的通用近似属性。我们表明，每当空间的指数函数界限时，每个函数都可以用浅神经网络近似于任何所需的精度。此结果随后导致根据指数函数的界限确定近似值的普遍性。此外，每当指数无限制时，我们就会为函数子空间获得一些表征，可以近似。
This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks with any desired accuracy. This result subsequently leads to determine the universality of the approximation depending on the boundedness of the exponent function. Furthermore, whenever the exponent is unbounded, we obtain some characterization results for the subspace of functions that can be approximated.
