Linear Hopfield networks and constrained optimization

It is shown that a Hopfield neural network (with linear transfer functions) augmented by an additional feedforward layer can be used to compute the Moore-Penrose generalized inverse of a matrix. The resultant augmented linear Hopfield network can be used to solve an arbitrary set of linear equations or, alternatively, to solve a constrained least squares optimization problem. Applications in signal processing and robotics are considered. In the former case the augmented linear Hopfield network is used to estimate the "structured noise" component of a signal and adjust the parameters of an appropriate filter on-line, whereas in the latter case it is used to implement an on-line solution to the inverse kinematics problem.