Neural network learning of optimal Kalman prediction and control.

Although there are many neural network (NN) algorithms for prediction and for control, and although methods for optimal estimation (including filtering and prediction) and for optimal control in linear systems were provided by Kalman in 1960 (with nonlinear extensions since then), there has been, to my knowledge, no NN algorithm that learns either Kalman prediction or Kalman control (apart from the special case of stationary control). Here we show how optimal Kalman prediction and control (KPC), as well as system identification, can be learned and executed by a recurrent neural network composed of linear-response nodes, using as input only a stream of noisy measurement data. The requirements of KPC appear to impose significant constraints on the allowed NN circuitry and signal flows.

Synchronous neural activity in scale-free network models versus random network models.

Synchronous firing peaks at levels greatly exceeding background activity have recently been reported in neocortical tissue. A small subset of neurons is dominant in a large fraction of the peaks. To investigate whether this striking behavior can emerge from a simple model, we constructed and studied a model neural network that uses a modified Hopfield-type dynamical rule.