Martin Burger, Andreas Neubauer,
"Error bounds for approximation with neural networks"
, in Journal of Approximation Theory, 2001, M. Burger and A. Neubauer, Error bounds for approximation with neural networks, J. Approx. Theory 112 (2001), 235-250.
Original Titel:
Error bounds for approximation with neural networks
Sprache des Titels:
Englisch
Englische Kurzfassung:
In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisfies an integral representation. We give error bounds not only in Hilbert spaces but in general Sobolev spaces. Finally, we apply our results to a class of perceptrons and present a sufficient smoothness condition
on f guaranteeing the integral representation.
Journal:
Journal of Approximation Theory
Erscheinungsjahr:
2001
Notiz zum Zitat:
M. Burger and A. Neubauer, Error bounds for approximation with neural networks, J. Approx. Theory 112 (2001), 235-250.