Unifying metric approach to the triple parity Original Research Article

The even-odd parity problem is a tough one for neural networks to handle because they assume a finite dimensional vector space. Typically, the size of the neural network increases as the size of the problem increases. The triple parity problem is even tougher. In this paper, a method is proposed for supervised and unsupervised learning to classify bit strings of arbitrary length in terms of their triple parity. The learner is modeled by two formal concepts, transformation system and stability optimization. Even though a small set of short examples were used in the training stage, all bit strings of any length were classified correctly in the online recognition stage. The proposed learner has successfully learned to devise a way by means of metric calculations to classify bit strings of any length according to their triple parity. The system was able to acquire the concept of counting, dividing, and then taking the remainder, by autonomously evolving a set of string-editing rules along with their appropriate weights to solve the difficult problem.