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

Problem
This paper addresses the limitations of high-capacity associative memory models, specifically Kernel Logistic Regression (KLR) Hopfield networks, which traditionally depend on synchronous updates that hinder their deployment on energy-efficient, event-driven neuromorphic hardware. The authors present a preprint that explores the asynchronous retrieval dynamics of KLR Hopfield networks, filling a gap in the literature regarding the operational efficiency of these models in practical applications.

Method
The core technical contribution of this work is the investigation of asynchronous sequential updates in KLR Hopfield networks. The authors empirically demonstrate that, with appropriately tuned kernel parameters, the trajectories of asynchronous updates are statistically indistinguishable from those of synchronous updates while maintaining high recall accuracy for random patterns. The study evaluates the network’s performance in terms of storage capacity, achieving empirical capacities of approximately ( P/N \approx 30 ) in static random pattern regimes, surpassing classical limits. The authors analyze the computational efficiency by measuring the total number of state transitions (bit flips) required for error correction, revealing that convergence occurs with a number of events closely aligned with the initial Hamming distance from the target pattern. This indicates that the KLR learning framework induces large-margin attractors, resulting in a smooth energy landscape conducive to sparse, event-driven computation.

Results
The asynchronous KLR Hopfield network demonstrates a storage capacity of ( P/N \approx 30 ), significantly exceeding the classical Hopfield limit of ( P/N \approx 0.15 ). The empirical results indicate that the network converges efficiently, requiring a number of state transitions proportional to the initial Hamming distance from the target pattern, with no observable spurious oscillations. These findings suggest that the asynchronous dynamics can effectively replicate the performance of synchronous updates while enhancing computational efficiency, making it suitable for neuromorphic implementations.

Limitations
The authors acknowledge that their findings are based on empirical evaluations and may not generalize across all types of patterns or noise conditions. They do not address the potential impact of varying kernel parameters on performance in real-world scenarios. Additionally, the study does not explore the scalability of the proposed method beyond the tested configurations, nor does it consider the implications of hardware-specific constraints in neuromorphic systems.

Why it matters
This work has significant implications for the development of low-power associative memory systems in neuromorphic computing. By demonstrating that KLR Hopfield networks can operate efficiently with asynchronous updates, the findings pave the way for more scalable and energy-efficient memory architectures. This could enhance the performance of various applications, including pattern recognition, associative retrieval, and other tasks requiring high-capacity memory in resource-constrained environments.

Authors: Akira Tamamori
Source: arXiv:2605.05978
URL: https://arxiv.org/abs/2605.05978v1