Coherent optical neural networks that have optical-frequency-controlled behavior and generalization ability in the frequency domain.

Coherent optical neural networks that have optical-frequency-controlled behavior are proposed as sophisticated optical neural systems. The coherent optical neural-network system consists of an optical complex-valued neural network, a phase reference path, and coherent detectors for selfhomodyne detection. The learning process is realized by adjusting the delay time and the transparency of neural connections in the optical neural network with the optical frequency as a learning parameter. Generalization ability in frequency space is also analyzed. Information geometry in the learning process is discussed for obtaining a parameter range in which a reasonable generalization is realized in frequency space. It is found that there are error-function minima periodically both in the delay-time domain and the input-signal-frequency domain. Because of this reason, the initial connection delay should be within a certain range for a meaningful generalization. Simulation experiments demonstrate that a stable learning and a reasonable generalization in the frequency domain are successfully realized in a parameter range obtained in the theory.