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
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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