Complex-valued neural networks (CVNNs) have become a powerful modelling tool for complex-valued data processing. Because most of the critical points of CVNNs are saddle points, the gradient-based learning algorithms for CVNNs enjoy more chances to reach the global minima while suffering from slow convergence. To this end, we propose a hybrid complex spectral conjugate gradient learning algorithm for fast training CVNNs in this paper. The proposed algorithm combines the scaled negative gradient with a Barzilai–Borwein stepsize and an optimized conjugate term to define a new training direction, thus providing an accurate approximation of the second-order curvature of the objective function. The complex Wolfe conditions are employed to adaptively determine the optimal training stepsize. Under mild conditions, the descent property of the training direction and the convergence of the proposed algorithm are theoretically established. Simulation results on a number of benchmark complex-valued data processing problems demonstrate the efficiency of the proposed algorithm.

中文翻译：

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用于复值数据处理的混合复谱共轭梯度学习算法

复值神经网络（CVNN）已成为复值数据处理的强大建模工具。由于 CVNN 的大多数关键点都是鞍点，因此基于梯度的 CVNN 学习算法有更多机会达到全局最小值，但收敛速度较慢。为此，我们在本文中提出了一种用于快速训练 CVNN 的混合复谱共轭梯度学习算法。所提出的算法将缩放负梯度与 Barzilai-Borwein 步长和优化共轭项相结合来定义新的训练方向，从而提供目标函数二阶曲率的精确近似。采用复杂的沃尔夫条件来自适应地确定最佳训练步长。在温和条件下，从理论上建立了训练方向的下降特性和算法的收敛性。对多个基准复值数据处理问题的仿真结果证明了该算法的效率。