TY - JOUR
T1 - A New Function Space from Barron Class and Application to Neural Network Approximation
AU - Meng , Yan
AU - Ming , Pingbing
JO - Communications in Computational Physics
VL - 5
SP - 1361
EP - 1400
PY - 2023
DA - 2023/01
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2022-0151
UR - https://global-sci.org/intro/article_detail/cicp/21367.html
KW - Fourier transform, Besov space, Sobolev space, radial function, neural network.
AB - <p style="text-align: justify;">We introduce a new function space, dubbed as the Barron spectrum space,
which arises from the target function space for the neural network approximation. We
give a Bernstein type sufficient condition for functions in this space, and clarify the
embedding among the Barron spectrum space, the Bessel potential space, the Besov
space and the Sobolev space. Moreover, the unexpected smoothness and the decaying
behavior of the radial functions in the Barron spectrum space have been investigated.
As an application, we prove a dimension explicit $L^q$ error bound for the two-layer
neural network with the Barron spectrum space as the target function space, the rate
is dimension independent.</p>