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