Associative memory by generalized holography

The concept of holography is generalized from idealized thick emulsion optical holography: to finite numbers of pixels, to other linear transforms than only the wave equation (using rectangular matrices), and to other non-linear recording functions. Using multiple exposures, two related computer simulations displaying auto-associative memory are demonstrated. These simulations consist of large, randomly connected, feed forward neural networks. This work is motivated by possible functioning of the brain’s memory and recognition. These simulations succeed in producing such associative memory based upon the statistics of large numbers and redundancy. They support arbitrarily large redundancies and fault tolerances. All memory is highly distributed. These simulations do not rely upon free-space assumptions, nor upon a wave equation. Information is assumed to be transmitted in a base-band manner, not through a carrier based manner (in contrast to optical holography). Some future directions are suggested.