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\begin{document}

\title{Approximation Error Estimates by Noise-injected Neural Networks}



\author[1]{Keito AKIYAMA}%
\affil[1]{Tohoku Daigaku - Aobayama Campus}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
One-hidden-layer feedforward neural networks are described as functions
having many real-valued parameters. The larger the number of parameters
is, neural networks can approximate various functions (universal
approximation property). The essential optimal order of approximation
bounds is already derived in 1996. We focused on the numerical
experiment that indicates the neural networks whose parameters have
stochastic perturbations gain better performance than ordinary neural
networks, and explored the approimation property of neural networks with
stochastic perturbations. In this paper, we derived the quantitative
order of variance of stochastic perturbations to achieve the essential
approximation order.%
\end{abstract}%



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