Smooth Function Approximation by Deep Neural Networks with General Activation Functions

Entropy

Yongdai Kim¹  Ilsang Ohn¹ 

[1] Department of Statistics, Seoul National University, Seoul 08826, Korea;

关键词: function approximation;    deep neural networks;    activation functions;    Hölder continuity;    convergence rates;   

DOI  :  10.3390/e21070627

来源: DOAJ

【 摘 要 】

There has been a growing interest in expressivity of deep neural networks. However, most of the existing work about this topic focuses only on the specific activation function such as ReLU or sigmoid. In this paper, we investigate the approximation ability of deep neural networks with a broad class of activation functions. This class of activation functions includes most of frequently used activation functions. We derive the required depth, width and sparsity of a deep neural network to approximate any Hölder smooth function upto a given approximation error for the large class of activation functions. Based on our approximation error analysis, we derive the minimax optimality of the deep neural network estimators with the general activation functions in both regression and classification problems.

【 授权许可】

Unknown