Dynamic Capacity Estimation in Hopfield Networks

TL;DR

This paper introduces a dynamic method for estimating the capacity of Hopfield networks, allowing for more accurate and efficient memory usage by monitoring and updating capacity in real-time during learning.

Contribution

The paper presents a novel dynamic capacity estimation model that operates concurrently with learning, improving accuracy and efficiency over static, worst-case estimates.

Findings

Capacity estimates are 93-97% accurate.

The model doubles memory efficiency compared to static estimates.

Reduces risk of overwriting stored patterns.

Abstract

Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic approach to monitoring a network's capacity. We define our understanding of capacity as the maximum number of stored patterns which can be retrieved when probed by the stored patterns. Prior work in this area has presented static expressions dependent on neuron count $N$, forcing network designers to assume worst-case input characteristics for bias and correlation when setting the capacity of the network. Instead, our model operates simultaneously with the learning Hopfield network and concludes on a capacity estimate based on the patterns which were stored. By continuously updating the crosstalk associated with the stored patterns, our model guards the network from overwriting its memory traces and exceeding its capacity. We simulate our model using artificially generated random patterns, which can be set to a desired bias and correlation, and observe capacity estimates between 93% and 97% accurate. As a result, our model doubles the memory efficiency of Hopfield networks in comparison to the static and worst-case capacity estimate while minimizing the risk of lost patterns.