Incorporating state space constraints into a neural network

We investigate the problem of constraining the dynamic trajectories of a continuous time neural network to a differentiable manifold in the network´s state space. This problem occurs in diverse application areas where the network states can be assigned a measure of quality or cost. In these cases we want to constrain the network to adhere to a manifold of high quality and low cost. We consider conditions which, if satisfied, guarantee that the network dynamics will not deviate from the desired manifold, and we illustrate the approach by showing how to incorporate a mechanism for learning linear manifold constraints into a recurrent backpropagation network. The resulting network can perform associative learning in conjunction with manifold learning