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

arXiv 2507.00461 ↗First posted 1 Jul 2025cs.NE cs.AIcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 10 of its 48 references that are in the map. First posted on arXiv 1 Jul 2025.

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10 of 48 references.

References · 10

  1. 2020Hopfield Networks is All You Needcited by 475
  2. 2017Deep Complex Networkscited by 217
  3. 2020Large Associative Memory Problem in Neurobiology and Machine Learningcited by 112
  4. 2020The universal approximation theorem for complex-valued neural networkscited by 28
  5. 2018Complex-valued Neural Networks with Non-parametric Activation Functionscited by 19
  6. 2019A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networkscited by 5
  7. 2020New Insights on Learning Rules for Hopfield Networks: Memory and Objective Function Minimisationcited by 5
  8. 2024Hierarchical Associative Memory, Parallelized MLP-Mixer, and Symmetry Breakingcited by 5
  9. 2025CVKAN: Complex-Valued Kolmogorov-Arnold Networkscited by 5
  10. 2025Dynamics of Structured Complex-Valued Hopfield Neural Networkscited by 1

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  1. 2026Toward Complex-Valued Neural Networks for Waveform Generation
  2. 2024BiPer: Binary Neural Networks using a Periodic Function
  3. 2024Modern Hopfield Networks Require Chain-of-Thought to Solve mathsfNC1-Hard Problems
  4. 2021BCNN: Binary Complex Neural Network
  5. 2022QONNX: Representing Arbitrary-Precision Quantized Neural Networks
  6. 2021Accurate Neural Training with 4-bit Matrix Multiplications at Standard Formats
  7. 2024Quantized Approximately Orthogonal Recurrent Neural Networks
  8. 2025iFairy: the First 2-bit Complex LLM with All Parameters in ±1, ± i