CONVERGENCE OF BACKWARD-ERROR-PROPAGATION LEARNING IN PHOTOREFRACTIVECRYSTALS

We analytically determine that the backward-error-propagation learning algorithm has a well-defined region of convergence in neural learning -parameter space for two classes of photorefractive-based optical neur al-network architectures. The first class uses electric-field amplitud e encoding of signals and weights in a fully coherent system, whereas the second class uses intensity encoding of signals and weights in an incoherent/coherent system. Under typical assumptions on the grating f ormation in photorefractive materials used in adaptive optical interco nnections, we compute weight updates for both classes of architectures . Using these weight updates, we derive a set of conditions that are s ufficient for such a network to operate within the region of convergen ce. The results are verified empirically by simulations of the XOR sam ple problem. The computed weight updates for both classes of architect ures contain two neural learning parameters: a learning-rate coefficie nt and a weight-decay coefficient. We show that these learning paramet ers are directly related to two important design parameters: system ga in and exposure energy. The system gain determines the ratio of the le arning-rate parameter to decay-rate parameter, and the exposure energy determines the size of the decay-rate parameter. We conclude that con vergence is guaranteed (assuming no spurious local minima in the error function) by using a sufficiently high gain and a sufficiently low ex posure energy per weight update. (C) 1996 Optical Society of America