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.