7,299 research outputs found
Pattern-recalling processes in quantum Hopfield networks far from saturation
As a mathematical model of associative memories, the Hopfield model was now
well-established and a lot of studies to reveal the pattern-recalling process
have been done from various different approaches. As well-known, a single
neuron is itself an uncertain, noisy unit with a finite unnegligible error in
the input-output relation. To model the situation artificially, a kind of 'heat
bath' that surrounds neurons is introduced. The heat bath, which is a source of
noise, is specified by the 'temperature'. Several studies concerning the
pattern-recalling processes of the Hopfield model governed by the
Glauber-dynamics at finite temperature were already reported. However, we might
extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in
terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo
method (the quantum MCMC), we analytically derive macroscopically deterministic
equations of order parameters such as 'overlap' in a quantum-mechanical variant
of the Hopfield neural networks (let us call "quantum Hopfield model" or
"quantum Hopfield networks"). For the case in which non-extensive number of
patterns are embedded via asymmetric Hebbian connections, namely,
for the number of neuron ('far from saturation'), we evaluate
the recalling processes for one of the built-in patterns under the influence of
quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI
Emerging Consciousness as a Result of Complex-Dynamical Interaction Process
A quite general interaction process within a multi-component system is analysed by the extended effective potential method, liberated from usual limitations of perturbation theory or integrable model. The obtained causally complete solution of the many-body problem reveals the phenomenon of dynamic multivaluedness, or redundance, of emerging, incompatible system realisations and dynamic entanglement of system components within each realisation. The ensuing concept of dynamic complexity (and related intrinsic chaoticity) is absolutely universal and can be applied to the problem of consciousness that emerges now as a high enough, properly specified level of unreduced complexity of a suitable interaction process. This complexity level can be identified with the appearance of bound, permanently localised states in the multivalued brain dynamics from strongly chaotic states of unconscious intelligence, by analogy with classical behaviour emergence from quantum states at much lower levels of world dynamics. We show that the main properties of this dynamically emerging consciousness (and intelligence, at the preceding complexity level) correspond to empirically derived properties of natural versions and obtain causally substantiated conclusions about their artificial realisation, including the fundamentally justified paradigm of genuine machine consciousness. This rigorously defined machine consciousness is different from both natural consciousness and any mechanistic, dynamically single-valued imitation of the latter. We use then the same, truly universal concept of complexity to derive equally rigorous conclusions about mental and social implications of the machine consciousness paradigm, demonstrating its indispensable role in the next stage of civilisation development
- âŠ