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Backgrond

June 2010

The development of physiological measurement technology in these decades brought about great impact on modeling and mathematical researches in neural networks. It is strongly expected that the new knowledge activates the engineering areas of neural networks. But in reality, we sometimes observe stagnation in these years.

Complex-valued neural networks (CVNNs), however, have continued to open doors to various new applications. The CVNNs are the neural networks that deal with complex amplitude, i.e. phase and amplitude, which is one of the most core concept in electrical and electronics engineering. A CVNN is never equivalent with a double-dimensional real-valued neural network. It has different dynamics and characteristics such as generalization, which is significantly useful in treatment of complex-amplitude information and wave-related phenomena. This is a critical point in applications in engineering fields. It is also crucial for developing new devices in the future. That is, the CVNN framework will play an important role in introduction of learning and self-organization into future quantum devices dealing with electron-wave and photonic wave.

We can further expect that broad-sense CVNNs such as quaternion neural networks break ground in unique directions appropriate for themselves respectively. Quaternion has been essential in computer graphics to render three-dimensional objects. When we introduce learning and self-organization in virtual realities and other computer-aided amenities, the quaternion neural networks will surely bring a fundamental framework. Furthermore, even in physiology, researchers suggest that the phase information of neuron firing timing against the theta wave in electroencephalogram possesses a close relationship to short-term memory in the brain.