Creative dynamics approach to neural intelligence

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Abstract
The thrust of this paper is to introduce and discuss a substantially new type of dynamical system for modelling biological behavior. The approach was motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks — their rigid behavior compared with even simplest biological systems. This approach exploits a novel paradigm in nonlinear dynamics based upon the concept of terminal attractors and repellers. It was demonstrated that non-Lipschitzian dynamics based upon the failure of Lipschitz condition exhibits a new qualitative effect — a multi-choice response to periodic external excitations. Based upon this property, a substantially new class of dynamical systems — the unpredictable systems — was introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously activated is based upon two pathological characteristics. Firstly, such systems have zero Jacobian. As a result of that, they have an infinite number of equilibrium points which occupy curves, surfaces or hypersurfaces. Secondly, at all these equilibrium points, the Lipschitz conditions fails, so the equilibrium points become terminal attractors or repellers depending upon the sign of the periodic excitation. Both of these pathological characteristics result in multi-choice response of unpredictable dynamical systems. It has been shown that the unpredictable systems can be controlled by sign strings which uniquely define the system behaviors by specifying the direction of the motions in the critical points. By changing the combinations of signs in the code strings the system can reproduce any prescribed behavior to a prescribed accuracy. That is why the unpredictable systems driven by sign strings are extremely flexible and are highly adaptable to environmental changes. It was also shown that such systems can serve as a powerful tool for temporal pattern memories and complex pattern recognition. It has been demonstrated that new architecture of neural networks based upon non-Lipschitzian dynamics can be utilized for modelling more complex patterns of behavior which can be associated with phenomenological models of creativity and neural intelligence.