Comparative Analysis of High-Order Rotor Hopfield Neural Networks and Dense Associative Memory: Structural Similarities and Functional Differences

This study presents a comparative analysis of Highorder Rotor Hopfield Neural Networks (HRHNNs) and Dense Associative Memory (DAM) models, highlighting their structural similarities and functional differences in associative memory tasks. Both models use energy functions to store patterns as lowenergy states, but they vary in handling multi-valued patterns and synaptic architectures. HRHNNs leverage high-order connections and multi-body synapses, which enhance their capacity for multivalued pattern storage and retrieval. In contrast, DAM operates with binary patterns and employs an energy difference learning algorithm. The experiments target multi-valued associative memory tasks for both HRHNNs and DAM. Results show that HRHNNs outperform DAM under high load factors and complex multi-valued tasks, while DAM demonstrates robustness with a larger number of patterns. This work emphasizes the potential of integrating biologically interpretable synaptic structures into artificial neural networks to enhance associative memory performance.