A constraint satisfaction theory for binary neural networks

Neural networks can be viewed as open constraint satisfaction networks. According to the consideration, neural networks (NNs) have to obey an inherent logical theory that consists of two-state decisions, weak constraints, rule type and strength, and identity and contradiction. This article presents the underlying frame of the theory that indicates that the essential reason why an NN is changing its states is the existence of superior contradiction inside the network, and that the process by which an NN seeks a solution corresponds to eliminating the superior contradiction. Different from general constraint satisfaction networks, the solutions found by NNs may contain inferior contradiction but not the superior contradiction. Accordingly, the constraints in NNs are weak or flexible. The ability of a general NN is insufficient for its application to constraint satisfaction problems.