Trained Hopfield neural networks need not be black-boxes

Neural networks are often criticised for being "black-boxes", in that their internal behaviour is hard to understand. In this paper, it is shown how the internal behaviour of trained Hopfield neural networks can be better understood, through analysis from a control theory viewpoint. The required techniques from control theory and differential geometry are presented. An explanation of why such analysis is important is provided, along with details of how nonlinear controllers can be produced using such analysis. The paper is concluded with an example, in which the internal behaviour of a trained Hopfield network is analysed using the techniques described.