Storage Capacity of Quaternion-Valued Hopfield Neural Networks With Dual Connections

Area of Science:

• Computational Neuroscience
• Artificial Intelligence
• Machine Learning

Background:

• Complex-valued Hopfield neural networks (CHNNs) are multistate models.
• Quaternion-valued Hopfield neural networks (QHNNs) were developed to reduce CHNN parameters.
• Dual connections (DCs) were introduced to QHNNs to enhance noise tolerance.

Purpose of the Study:

• To investigate the impact of the ebbian rule on the storage capacity of QHNNs with DCs.
• To address the reduced storage capacity issue in QHNNs with DCs.

Main Methods:

• Introduction of the ebbian rule to QHNNs with DCs.
• Stochastic analysis to prove the storage capacity improvement.
• Comparison of storage capacity with CHNNs and conventional QHNNs.

Main Results:

• QHNNs with DCs offer superior noise tolerance compared to CHNNs.
• The ebbian rule increases the storage capacity of QHNNs with DCs to 0.8 times that of CHNNs.
• The architecture of QHNNs with DCs is not the cause of limited storage capacity.

Conclusions:

• The ebbian rule effectively enhances the storage capacity of QHNNs with DCs.
• QHNNs with DCs, when utilizing the ebbian rule, present a promising alternative for complex associative memory tasks.
• Further research into novel learning rules can optimize QHNN performance.