Local and asymmetric interconnections using volume holograms
Xiang-Guang Gu, Demetri Psaltis · Annual Meeting Optical Society of America · 1988
Volume holograms provide the possibility for very high density storage of the interconnecting weights in an optical neural computer. The number of connections that can be stored in a hologram of volume V can approach N3 = O(V/λ 3 ). We have shown previously how N3/2 out of N2 pixels can be selected as fractal sampling grids at the input and output planes so that all connections can be independently implemented by the volume hologram. We derive the sampling grids for arbitrary N d →N 3–d mappings for any 1 ⪯ d ⪯ 2, and we extend these ideas to the use of volume holograms for the implementation of local connectivity. If each pixel in a 2-D array of M units is to be arbitrarily interconnected to its C neighbors, the total number of connections is MC. We show that the volume required for the implementation of the local connectivity scheme we describe is O(MC).