用全息光路实现高密度联想记忆,光学计算精确模拟现代霍普菲尔德模型。
Dense Holographic Associative Memories

- 两片全息镜加一维编码层构成光学计算结构,实现霍普菲尔德模型的精确映射。
- 通过非局域梯度响应介质,存储效率提升至线性 $M^{-1}$,突破传统材料的 $M^{-2}$ 限制。
- 适合光学神经网络、高速联想存储系统研究者,为硬件实现新型神经模型提供路径。
联想回忆——将一个输入模式映射到最相似的已存储模式——是高维视觉前端的天然计算原语,恰好也是体全息图原生执行的操作。我们证明,由一片体全息图与一维编码层分隔的级联结构,能通过并行光学计算精确实现现代霍普菲尔德(密集联想记忆)的检索映射 $η = V ext{softmax}(λK^T x)$,其中逆温度通过编码层的光控空间光调制实现。将输入输出经由一维编码而非直接在二维平面间传输,提供了原始霍普菲尔德模型缺失的分离非线性,并通过平衡光栅波矢量维度($2+1=3$)消除了直接二维到二维全息图中的布拉格退化问题,避免了分形采样。忠实的密集存储要求记录介质能捕获神经元间连接,同时抑制导致均匀光电折射材料效率下降 $M^{-2}$ 的场自能。我们提出一种非局域、梯度响应介质,其光照无关衰减可原位恢复线性 $M^{-1}$ 效率,并在离散对向二极管单元中演示了其接收、组合与存储功能。文中还概述了基于OASLM堆栈及体分子/纳米晶体实现的路径。
原文摘要 · Abstract (English)
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, $η= V \text{softmax}(λK^T x)$, 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.
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