Error-corrective optical neural networks modelled by persistent spectral hole-burning

Abstract

We show that materials with the ability to form persistent spectral holes under illumination have frequency as an additional optically parallel accessible degree of freedom that may be incorporated into associative memory. This opens new possibilities for increasing the number of interconnections in optical models of neural networks. In our first example, a 144-element autoassociative memory matrix is constructed on two 12-bit vectors and has two dimensions (x and frequency ω). The probe vector at the memory input carries two erroneous bits (out of 12 bits) and is onedimensional (spatial coordinate x); the memory output-with the error bits correctedis one-dimensional in frequency ω. The second example uses memory input that is twodimensional (image in coordinates x, y); the memory matrix is four-dimensional (x, y ω, t), where t (time coordinate) is given by the temporal delay of photochemically accumulated stimulated photon echo signal; memory output is two-dimensional (ω and t) and corrects two bits out of the 12-bit vector. In the third example, quadratic autoassociative memory is coded in three dimensions (coordinates x, y, ω) and materializes 32×32×32=32768 optical interconnections; the probe vector is given as a 32×32 spatial matrix (coordinates x, y); the output is one-dimensional, consists of 32 bits along the frequency axis, and corrects four erroneous bits.