A multivalued bidirectional associative memory operating on a complex domain

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Neuroscience

Background:

• Bidirectional Associative Memory (BAM) models are crucial for pattern recognition and associative recall.
• Existing BAM models often utilize real-valued states and weights, limiting their representational capacity.
• Complex-valued systems offer enhanced capabilities in signal processing and information storage.

Purpose of the Study:

• To introduce and analyze a novel Complex Domain Bidirectional Associative Memory (CDBAM).
• To demonstrate the stability and convergence properties of the proposed CDBAM.
• To develop a gradient descent algorithm for designing the weight matrix of CDBAM.

Main Methods:

• Investigated a BAM with complex states and connection weights, where states are quantized values on the complex plane's unit circle.
• Utilized a Lyapunov function to prove bidirectional stability for both synchronous and asynchronous operations.
• Derived a gradient descent algorithm in the complex domain for weight matrix design.

Main Results:

• The proposed Complex Domain Bidirectional Associative Memory (CDBAM) is proven to be bidirectionally stable.
• All equilibrium points of CDBAM correspond to local energy minima.
• A gradient descent algorithm effectively designs the weight matrix for CDBAM.

Conclusions:

• The CDBAM offers enhanced stability and convergence properties compared to traditional BAMs.
• The gradient descent algorithm provides an efficient method for designing complex-valued associative memories.
• Computer simulations validate the CDBAM's performance, capacity, and applicability.