TY - JOUR
T1 - Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
AU - Siegel, Jonathan W.
AU - Xu, Jinchao
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/6
Y1 - 2023/6
N2 - We study the variation space corresponding to a dictionary of functions in L2(Ω) for a bounded domain Ω ⊂ Rd. Specifically, we compare the variation space, which is defined in terms of a convex hull with related notions based on integral representations. This allows us to show that three important notions relating to the approximation theory of shallow neural networks, the Barron space, the spectral Barron space, and the Radon BV space, are actually variation spaces with respect to certain natural dictionaries.
AB - We study the variation space corresponding to a dictionary of functions in L2(Ω) for a bounded domain Ω ⊂ Rd. Specifically, we compare the variation space, which is defined in terms of a convex hull with related notions based on integral representations. This allows us to show that three important notions relating to the approximation theory of shallow neural networks, the Barron space, the spectral Barron space, and the Radon BV space, are actually variation spaces with respect to certain natural dictionaries.
UR - http://www.scopus.com/inward/record.url?scp=85148507303&partnerID=8YFLogxK
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U2 - 10.1007/s00365-023-09626-4
DO - 10.1007/s00365-023-09626-4
M3 - Article
AN - SCOPUS:85148507303
SN - 0176-4276
VL - 57
SP - 1109
EP - 1132
JO - Constructive Approximation
JF - Constructive Approximation
IS - 3
ER -