High-capacity associative memory models, such as Kernel Logistic Regression (KLR) Hopfield networks, have demonstrated strong storage capabilities but typically rely on computationally expensive synchronous updates. This reliance poses a bottleneck for deployment on energy-efficient, event-driven neuromorphic hardware. In this paper, we investigate the asynchronous retrieval dynamics of KLR Hopfield networks. We show empirically that, under appropriately tuned kernel parameters, asynchronous sequential updates exhibit trajectories that are statistically indistinguishable from those of synchronous dynamics, while maintaining high recall accuracy within the tested regime for random patterns. Furthermore, we find that the asynchronous network achieves empirical storage capacities approaching $P/N \approx 30$ in static random pattern regimes, exceeding classical limits. To evaluate computational efficiency, we analyze the total number of state transitions (bit flips) required for error correction. The results show that the network converges using a number of events close to the initial Hamming distance from the target pattern, without observable spurious oscillations. These findings suggest that the large-margin attractors induced by KLR learning create a smooth energy landscape suited for sparse, event-driven computation, providing a basis for scalable and low-power associative memory on neuromorphic architectures.

翻译：高容量联想记忆模型，如核逻辑回归(KLR)霍普菲尔德网络，已展现出强大的存储能力，但通常依赖于计算成本高昂的同步更新。这种依赖关系制约了其在高效节能、事件驱动的神经形态硬件上的部署。本文研究了KLR霍普菲尔德网络的异步检索动力学。我们通过实验证明，在适当调优核参数下，异步时序更新展现出的轨迹在统计上与同步动力学不可区分，同时在随机模式的测试范围内保持高召回精度。此外，我们发现异步网络在静态随机模式场景下达到了接近$P/N \approx 30$的经验存储容量，超越了经典极限。为评估计算效率，我们分析了纠错所需的总状态转换次数（比特翻转）。结果表明，网络收敛所需的事件数接近初始与目标模式的汉明距离，且未观察到虚假振荡。这些发现表明，KLR学习诱导的大间隔吸引子形成了适合稀疏事件驱动计算的光滑能量景观，为在神经形态架构上实现可扩展、低功耗的联想记忆奠定了坚实基础。