Optical associative memory with invariances

A single-slab second order neural network model with scale and translation invariances is proposed. This is based on the backpropagation learning rule by using group theory to impose the invariances to the network. The results show that full range translation invariance and a limited range of scale invariance are realisable. The performance of outer-product model with invariance is analysed. Then an inner-product associative memory model with translation invariance is proposed. A strictly increasing nonlinear operation which is cooperated with a sign function is chosen to guarantee the correct recall convergence of the network without iteration. The performance of network is improved drastically. These two models can be implemented by simple optical systems with parallel processing capability