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

2026-05-07

AI Summary

This work addresses the challenge of deploying high-capacity kernel Hopfield networks on event-driven neuromorphic hardware, which is hindered by their reliance on synchronous updates. The study investigates the asynchronous retrieval dynamics of kernel logistic regression–based Hopfield networks and demonstrates that, through careful tuning of kernel parameters, asynchronous sequential updates become statistically equivalent to their synchronous counterparts while preserving high recall accuracy. For the first time, it is shown that asynchronous dynamics can operate stably at storage capacities approaching \( P/N \approx 30 \), surpassing the classical Hopfield limit, and exhibit a smooth energy landscape amenable to event-driven computation. The number of state transitions required for convergence scales approximately with the initial Hamming distance, without significant spurious oscillations, enabling efficient and low-power associative memory retrieval.

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.

Problem

• event-driven
• associative memory
• Hopfield networks
• neuromorphic hardware
• asynchronous retrieval

Innovation

• asynchronous retrieval
• kernel Hopfield networks
• neuromorphic computing
• high-capacity associative memory
• event-driven dynamics