@article{875897dcea834103874f7aae978899e0,

title = "An integral representation of functions using three-layered networks and their approximation bounds",

abstract = "Neural networks are widely known to provide a method of approximating nonlinear functions. In order to clarify its approximation ability, a new theorem on an integral transform of ridge functions is presented. By using this theorem, an approximation bound, which evaluates the quantitative relationship between the approximation accuracy and the number of elements in the hidden layer, can be obtained. This result shows that the approximation accuracy depends on the smoothness of target functions. It also shows that the approximation methods which use ridge functions are free from the 'curse of dimensionality'.",

keywords = "approximation bound, curse of dimensionality, integral transform, random coding, ridge function, three-layered network",

author = "Noboru Murata",

note = "Funding Information: The author would like to give very special thanks to the review for his useful comments simplifying the proofs and his careful examination of the manuscript. The author would like to thank Professor S. Amari, Professor S. Yoshizawa, Dr K. R. M{\"u}ller and D. Harada for helpful suggestions and discussions. The present work is supported in part by Grant-in-Aid for Scientific Research in Priority Areas on Higher-Order Brain Information Processing from the Ministry of Education, Science and Culture of Japan. ",

year = "1996",

month = aug,

doi = "10.1016/0893-6080(96)00000-7",

language = "English",

volume = "9",

pages = "947--956",

journal = "Neural Networks",

issn = "0893-6080",

publisher = "Elsevier Limited",

number = "6",

}