Kavli Affiliate: Wei Gao
| First 5 Authors: Shao-Qun Zhang, Wei Gao, Zhi-Hua Zhou, ,
| Summary:
Complex-valued neural networks have attracted increasing attention in recent
years, while it remains open on the advantages of complex-valued neural
networks in comparison with real-valued networks. This work takes one step on
this direction by introducing the emph{complex-reaction network} with
fully-connected feed-forward architecture. We prove the universal approximation
property for complex-reaction networks, and show that a class of radial
functions can be approximated by a complex-reaction network using the
polynomial number of parameters, whereas real-valued networks need at least
exponential parameters to reach the same approximation level. For empirical
risk minimization, our theoretical result shows that the critical point set of
complex-reaction networks is a proper subset of that of real-valued networks,
which may show some insights on finding the optimal solutions more easily for
complex-reaction networks.
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