Towards Understanding Theoretical Advantages of Complex-Reaction Networks

• URL: http://arxiv.org/abs/2108.06711v1
• Date: Sun, 15 Aug 2021 10:13:49 GMT
• Title: Towards Understanding Theoretical Advantages of Complex-Reaction Networks
• Authors: Shao-Qun Zhang, Gao Wei, Zhi-Hua Zhou
• Abstract summary: We show that a class of functions can be approximated by a complex-reaction network using the number of parameters. 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.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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