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：高容量关联记忆模型，例如核逻辑回归（KLR）霍普菲尔德网络，已展现出强大的存储能力，但通常依赖于计算密集型同步更新。这种依赖性为将其部署到节能、事件驱动的神经形态硬件上造成了瓶颈。本文研究了KLR霍普菲尔德网络的异步检索动态。我们通过实验证明，在适当调整核参数的情况下，异步顺序更新的轨迹在统计上与同步动态的轨迹无法区分，同时在随机模式的测试范围内保持了高召回准确率。此外，我们发现异步网络在静态随机模式场景下实现了经验存储容量接近$P/N \approx 30$，超过了经典极限。为评估计算效率，我们分析了纠错所需的总状态转换（比特翻转）次数。结果表明，网络在接近目标模式的初始汉明距离下收敛，且未观察到明显的虚假振荡。这些发现表明，KLR学习产生的大间隔吸引子形成了适合稀疏、事件驱动计算的平滑能量景观，为神经形态架构上可扩展、低功耗的关联记忆提供了基础。