Biological evidence shows that there are neural networks specialized for recognition of signals and patterns acting as associative memories. The spiking neural networks are another kind which receive input from a broad range of other brain areas to produce output that selects particular cognitive or motor actions to perform. An important contribution of this work is to consider the geometric processing in the modeling of feed-forward neural networks. Since quaternions are well suited to represent 3D rotations, it is then well justified to extend real-valued neural networks to quaternion-valued neural networks for task of perception and control of robot manipulators. This work presents the quaternion spiking neural networks which are able to control robots, where the examples confirm that these artificial neurons have the capacity to adapt on-line the robot to reach the desired position. Also, we present the quaternionic quantum neural networks for pattern recognition using just one quaternion neuron. In the experimental analysis, we show the excellent performance of both quaternion neural networks.

中文翻译：

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四元数尖峰和四元数量子神经网络：理论与应用

生物学证据表明，存在专门用于识别充当联想记忆的信号和模式的神经网络。尖峰神经网络是另一种类型，它从广泛的其他大脑区域接收输入以产生选择特定认知或运动动作来执行的输出。这项工作的一个重要贡献是考虑了前馈神经网络建模中的几何处理。由于四元数非常适合表示 3D 旋转，因此有理由将实值神经网络扩展到四元值神经网络，以完成机器人操纵器的感知和控制任务。这项工作提出了能够控制机器人的四元数脉冲神经网络，这些例子证实了这些人工神经元有能力在线调整机器人以达到所需的位置。此外，我们还展示了仅使用一个四元数神经元的模式识别四元数量子神经网络。在实验分析中，我们展示了两种四元数神经网络的优异性能。