Abstract: The authors have previously proposed a network of probabilistic cellular automata (PCAs) as part of an image recognition system designed to integrate model-based and data-driven approaches in a connectionist framework. The PCA arises from some natural requirements on the system which include incorporation of prior knowledge such as in inference rules, locality of inferences, and full parallelism. This network has been applied to recognize objects in both synthetic and in real data. This approach achieves recognition through the short-, rather than the long-time behavior of the dynamics of the PCA. In this paper, some methods are developed for learning the connection strengths by solving linear inequalities: the figures of merit are tendencies or directions of movement of the dynamical system. These $PRM@dynamical$PRM figures of merit result in inequality constraints on the connection strengths which are solved by linear (LP) or quadratic programs (QP). An algorithm is described for processing a large number of samples to determine weights for the PCA. The work may be regarded as either pointing out another application for constrained optimization, or as pointing out the need to extend the perceptron and similar methods for learning. The extension is needed because the neural network operates on a different principle from that for which the perceptron method was devised.!
展开▼
