Efficient event-driven retrieval in high-capacity kernel Hopfield networks

TL;DR

This paper demonstrates that asynchronous updates in high-capacity Kernel Logistic Regression Hopfield networks can achieve near-synchronous performance, high storage capacity, and efficient, event-driven retrieval suitable for neuromorphic hardware.

Contribution

It empirically shows that asynchronous dynamics match synchronous ones in KLR Hopfield networks, enabling scalable, low-power associative memory implementations.

Findings

Asynchronous updates produce trajectories similar to synchronous ones.

Storage capacity approaches P/N ≈ 30, exceeding classical limits.

Network converges with event counts close to initial Hamming distance.

Abstract

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.