On the training and the convergence of brain-state-in-a-box neural networks

It is the aim of the paper to contribute to the understanding and applicability of brain-state-in-a-box neural networks. It is shown how asymmetric brain-state-in-a-box neural networks achieve a multiple objective optimization, generalizing the `energy´-interpretation of symmetric neural networks. It is therefore expected that asymmetric neural networks will have interesting applications once the dynamic behaviour is sufficiently mastered. The theorems in the paper contribute to this goal by giving conditions that guarantee uniqueness and global stability of the equilibrium. In addition, an adaptive algorithm was given for training this type of neural networks