Self-organized artificial neural networks with novel phase transition learning rule for solving bistable reversible figures and XOR problems

This writing wishes to apply the phase transition cooperative phenomena to neurocomputing. Specifically the collaborated H. Haken synergetic computer theory and Per Bak self-organized criticality theory will be adapted to artificial neural network models for the applications in image processing, pattern recognition, self-architecture neural networks and information processing. An artificial perceptron neural network model is proposed to explain the multistable perception in "reversible figures". The networks are composed of a shifting invariant smart eye preprocessing unit, a depth processing unit and the main brain computing unit. The main brain computing network is a revised back error propagation network. A polynomial energy function is used for the performance measure replacing the least mean square energy. The test of "reversible figures" is subsequently controlled by the phase transition tuning parameter driven bottom up from test image data. The effects of the tuning parameter are illustrated, and the modeling of multistable perception is discussed. It is demonstrated that the brain computing networks trained with the new energy function generally have better performance in training speed and classification of patterns than the standard back error propagation networks trained by the least mean square energy function. The behavior of a self-architecting neural network with a new phase transition learning rule is investigated. This model is based on Adaptive Performance Network purposed by Stassinopoulos, Alstrom, and Bak with two significant modifications: An L$\sp1$ energy function and a non-unity energy threshold in the weight update equation are articulated; Instar instead of the outstar normalization is performed. The simulation indicates that the basic structure of an APN is quite tolerant to the learning rule changes of its composing elements, it also showed that even at the converged state the performance of the revised APN model exhibits much random fluctuation resembling the l/f power spectrum law. These characteristics are the main signature of the Per Bak self-organized criticality state.