Associative memory systems enable content-addressable storage and retrieval of patterns, a capability central to biological neural computation and artificial intelligence. Classical implementations such as Hopfield networks face fundamental limitations in memory capacity, scaling at most linearly with network size. We present an associative memory architecture based on Kuramoto oscillator networks with honeycomb topology in which memories are encoded as stable phase-locked configurations. The honeycomb network consists of multiple cycles that share nodes in a chain-like arrangement, creating a one-dimensional lattice of chained+loops. We prove that this architecture achieves exponential memory capacity: a network of $N$ oscillators can store $(2\lceil n_c/4 \rceil - 1)^m$ distinct patterns, where $m$ honeycomb cycles each contain $n_c$ oscillators. Moreover, we fully characterize all stable configurations and prove that each memory's basin of attraction maintains a guaranteed minimum size independent of network scale. Simulations using charge-density-wave (CDW) oscillators validate predicted phase-locking behavior, demonstrating practical realizability in neuromorphic hardware.

翻译：联想记忆系统支持内容的可寻址存储与模式检索，这一能力是生物神经计算与人工智能的核心。经典实现如Hopfield网络在记忆容量上存在根本性限制，其规模最多随网络大小线性增长。我们提出了一种基于Kuramoto振荡器网络与蜂窝拓扑的联想记忆架构，其中记忆被编码为稳定的锁相配置。该蜂窝网络由多个共享节点的循环以链状排列构成，形成一维链式环格点结构。我们证明了该架构可实现指数级记忆容量：包含$N$个振荡器的网络可存储$(2\lceil n_c/4 \rceil - 1)^m$个不同模式，其中$m$个蜂窝循环各包含$n_c$个振荡器。此外，我们完整刻画了所有稳定配置，并证明每个记忆的吸引域保持与网络规模无关的保证最小尺寸。采用电荷密度波（CDW）振荡器的仿真验证了预测的锁相行为，证明了其在神经形态硬件中的实际可实现性。