STOCHASTIC DYNAMICS OF NETWORKS WITH SEMICLASSICAL EXCITATIONS

Abstract

As artificial intelligence seems destined to go for devices at the nano-scale level involving quantized interactions, we investigate the changes brought forth by a transition of a dynamical classical neural system to a quantum one. First, we consider cases of interaction between neurons and with an external source, which are analytically tractable, and find relations for their average times of transition between different quantum states. We get simple relations between the average transition time and the effective potential in limits of resonance and small damping. Such potentials, with harmonic and/or damped behavior, may be quite important in nanoelectronic devices. We then present a network set up with interactions between nodes similar to classical biological-like action potentials with finite durations, and compare it with the classical integrate-and-fire neural network. As in the classical systems, we obtain from such networks dynamical behavior differing according to the type of static input. We have examined the role of the novel stochasticity introduced by the quantum potential which fuzzifies the logical links, in contrast to the system with the deterministic classical neural network. The dynamic quantum system also shows oscillations similar to biological systems. The average periodic behavior of the system, as found from simulations, agrees remarkably well with a simple formula with a single parameter to account for the intrinsic randomness of the system. Short-term retentivity of input memory is observed to be subtle but perceptible, and may be useful in designing devices with quantum networks that need a gradual auto-erasing facility, which too, being quasi-biological, may be a desirable feature in systems trying to mimic living neural systems.