On the approximation of functions by tanh neural networks
FOS: Computer and information sciences
Function approximation
Computer Science - Machine Learning
Tanh
Deep learning
Numerical Analysis (math.NA)
02 engineering and technology
01 natural sciences
Machine Learning (cs.LG)
Neural networks; Tanh; Function approximation; Deep learning
FOS: Mathematics
0202 electrical engineering, electronic engineering, information engineering
Mathematics - Numerical Analysis
Neural Networks, Computer
0101 mathematics
Neural networks
DOI:
10.1016/j.neunet.2021.08.015
Publication Date:
2021-08-19T17:47:18Z
AUTHORS (3)
ABSTRACT
We derive bounds on the error, in high-order Sobolev norms, incurred in the approximation of Sobolev-regular as well as analytic functions by neural networks with the hyperbolic tangent activation function. These bounds provide explicit estimates on the approximation error with respect to the size of the neural networks. We show that tanh neural networks with only two hidden layers suffice to approximate functions at comparable or better rates than much deeper ReLU neural networks.<br/>Neural Networks, 143<br/>
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