Dense Holographic Associative Memories

Abstract

Associative recall -- mapping an incident pattern to the stored one it most resembles -- is the natural computational primitive of a high-dimensional vision front end, and it is precisely the operation a volume hologram performs natively. We show that a cascade of two volume holograms separated by a one-dimensional coded layer physically evaluates the modern Hopfield (dense associative memory) retrieval map, $\hat{I}\cdot =V\text{softmax}(\hat{I}»K^{T}x)$, exactly as a parallel optical computation, with the inverse temperature realized via optically addressed spatial light modulation in the coded-layer. Routing the input and output through a 1D code rather than directly between 2D planes supplies the separating nonlinearity the original Hopfield model lacked and, by balancing the grating-wavevector dimension count ($2+1=3$), removes the Bragg degeneracy that otherwise forces fractal sampling on a direct 2D-to-2D hologram. Faithful dense storage further demands a recording medium that captures inter-neuron connections while rejecting the field self-energy responsible for the $M^{-2}$ efficiency falloff of homogeneous photorefractives. We propose a nonlocal, gradient-responsive medium whose illumination-independent decay recovers the linear $M^{-1}$ scaling in situ, and demonstrate its reception, combination, and storage functions in a discrete opposing-diode cell. Routes to OASLM-stack and volume molecular/nanocrystal realizations are outlined.