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arXiv · 2108.06711

Towards Understanding Theoretical Advantages of Complex-Reaction Networks

Shao-Qun Zhang·Wei Gao·Zhi-Hua Zhou
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Abstract

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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Shao-Qun Zhang, Wei Gao, Zhi-Hua Zhou. 2021-08-15. Towards Understanding Theoretical Advantages of Complex-Reaction Networks. https://doi.org/10.1016/j.neunet.2022.03.024

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