The bit generator and time-series prediction

We study the dynamics of the Bit-Generator: a perceptron where in each time step the input units are shifted one bit to the right with the state of the leftmost input unit set equal to the output unit in the previous time step. The longtime behavior of the Bit-Generator consists of cycles whose typical period scales polynomially with the size of the network and whose spatial structure is periodic with a typical finite wave length. We investigate the problem of training one Bit-Generator to mimic another. The generalization error on a cycle is zero for a finite training set and global dynamical behaviors can also be learned in a finite time. Hence, a pro jection of a rule can be learned in a finite time.