Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks

Xu Dongpo; Dong Jian; Zhang Chengdong

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Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks

机译：完全复值神经网络的拟牛顿法的收敛性

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摘要

In this paper, based on Wirtinger calculus, we introduce a quasi-Newton method for training complex-valued neural networks with analytic activation functions. Using the duality between Wirtinger calculus and multivariate real calculus, we prove a convergence theorem of the proposed method for the minimization of real-valued complex functions. This lays the theoretical foundation for the complex quasi-Newton method and generalizes Powell's well-known result for the real-valued case. The simulation results are given to show the effectiveness of the method.

机译：本文基于Wirtinger演算，介绍一种准牛顿法，用于训练具有解析激活函数的复值神经网络。利用Wirtinger演算和多元实数演算之间的对偶性，我们证明了所提出方法的最小化实值复数函数的收敛定理。这为复拟牛顿法奠定了理论基础，并推广了鲍威尔对于实值情形的著名结果。仿真结果表明了该方法的有效性。

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来源
《Neural processing letters》 |2017年第3期|961-968|共8页
作者
Xu Dongpo; Dong Jian; Zhang Chengdong;
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作者单位

Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China;

Harbin Engn Univ, Coll Sci, Harbin 150001, Heilongjiang, Peoples R China;

Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Jilin, Peoples R China;

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正文语种 eng
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关键词
Complex-valued neural networks; Complex-valued DFP formula; Quasi-Newton method; Wirtinger calculus; Convergence analysis;

机译：复值神经网络复值DFP公式拟牛顿法Wirtinger演算收敛性分析;

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2. Deterministic convergence of complex mini-batch gradient learning algorithm for fully complex-valued neural networks [J] . Zhang Huisheng, Zhang Ying, Zhu Shuai, Neurocomputing . 2020,第Sepa24期

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3. Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays [J] . Tang Qian, Jian Jigui Mathematics and computers in simulation . 2019,第MAY期

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4. Quasi-Newton learning methods for complex-valued neural networks [C] . Popa Calin-Adrian International Joint Conference on Neural Networks . 2015

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5. Newton's method backpropagation for complex-valued holomorphic neural networks: Algebraic and analytic properties. [D] . La Corte, Diana Thomson. 2014

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6. Multi-Sensor Data Fusion Identification for Shearer Cutting Conditions Based on Parallel Quasi-Newton Neural Networks and the Dempster-Shafer Theory [O] . Lei Si, Zhongbin Wang, Xinhua Liu, 2015

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7. Convergence of an Online Split-Complex Gradient Algorithm for Complex-Valued Neural Networks [O] . Huisheng Zhang, Dongpo Xu, Zhiping Wang 2010

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8. Improved Landmine Detection by Complex-Valued Artificial Neural Networks [R] . Bose, N. K. 2002

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Convergence of Quasi-Newton Method for Fully Complex-Valued Neural Networks

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