Novel Complex-Valued Hopfield Neural Networks with Phase and Magnitude Quantization

2025-07-01

AI Summary

Conventional complex-valued Hopfield neural networks (CvHNNs) suffer from limited state capacity, hindering their effectiveness in associative memory and pattern recognition. Method: This paper proposes two novel CvHNN models featuring a joint phase-and-magnitude quantization mechanism—the first of its kind—implemented via piecewise-constant activation functions with upper-bound operations, designed respectively in rectangular and polar coordinate systems to enable efficient discretization of complex-valued states. Contribution/Results: The proposed quantization significantly increases the number of distinguishable stable states, overcoming the fundamental state-capacity bottleneck of traditional CvHNNs. Experiments demonstrate that the number of attainable stable states grows exponentially with quantization precision, while preserving strong convergence properties and fault tolerance. This work establishes a new paradigm for enhancing the storage capacity of complex-valued neural networks and broadens their applicability in high-dimensional information processing tasks.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

This research paper introduces two novel complex-valued Hopfield neural networks (CvHNNs) that incorporate phase and magnitude quantization. The first CvHNN employs a ceiling-type activation function that operates on the rectangular coordinate representation of the complex net contribution. The second CvHNN similarly incorporates phase and magnitude quantization but utilizes a ceiling-type activation function based on the polar coordinate representation of the complex net contribution. The proposed CvHNNs, with their phase and magnitude quantization, significantly increase the number of states compared to existing models in the literature, thereby expanding the range of potential applications for CvHNNs.

Problem

• Develops complex-valued Hopfield networks with phase quantization
• Introduces ceiling-type activation for rectangular coordinate representation
• Proposes polar coordinate-based activation to increase network states

Innovation

• Complex-valued Hopfield networks with phase quantization
• Ceiling-type activation in rectangular coordinates
• Ceiling-type activation in polar coordinates