A Neuromorphic Computational Model for Spintronics-based Hopfield Oscillatory Neural Network

Sandeep Soni; Yasser Rezaeiyan; Tim Boehnert; Ricardo Ferreira; Brajesh Kumar Kaushik; Farshad Moradi; Sonal Shreya

doi:10.1109/TMAG.2025.3539977

A Neuromorphic Computational Model for Spintronics-based Hopfield Oscillatory Neural Network

Sandeep Soni^*, Yasser Rezaeiyan, Tim Boehnert, Ricardo Ferreira, Brajesh Kumar Kaushik, Farshad Moradi^*, Sonal Shreya^*

^*Corresponding author for this work

Department of Electrical and Computer Engineering - Electronics and Photonics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

The human brain is competent in information processing and learning, largely due to the coordinated activity of neuronal populations. These populations exhibit rhythmic fluctuations in activity known as oscillatory dynamics, observed across different brain regions. These oscillations are crucial in various cognitive functions, such as memory consolidation, sensory processing, and motor control. This work proposes a novel neuromorphic computational (NC) model comprising analytical derivation for a spintronics-based Hopfield oscillatory neural network (HONN) employing frequency synchronization inspired by the brain's oscillatory mechanism of pattern recognition and associative memory. Kuramoto model, which represents the phase-based coupling of two oscillators, this work presents an extended mathematical analysis (modeling) of frequency and phase-based dual coupling mechanism. Further, this model is translated to the Theile equation which governs the dynamics of magnetic vortex core (such as core position and oscillation frequency) applicable to spintronic-based HONN. This approach uses spin-torque vortex nano-oscillators (SVNOs) as neurons connected via resistive synapses representing synaptic coupling strength. The model describes the analytical relation between the SVNOs and the synaptic element, and how it influences the synchronized frequency (fsync). Stronger coupling aligns fsync closer to the higher gyrotropic frequency of the magnetic vortex core within the network, while weaker coupling promotes fsync closer to the lower one. The synaptic connections transition between low resistance (LRS) and high resistance (HRS) states mimicking biological brain plasticity. This NC model is then utilized to design a spintronic-based HONN circuit to illustrate oscillatory properties, frequency-based synchronization, and resistive coupling to create an energy-efficient and scalable architecture. The proposed NC model represents a promising approach to advancing large-scale HONN hardware architecture, particularly by enabling the integration of SVNOs as neurons, resistive memories as synapses, and conventional electronics as peripherals. This model serves as a foundational framework for exploring the feasibility, functionality, and reliability of advanced neural network architectures, crucial for evaluating the potential of these hybrid systems in practical, large-scale applications.

Original language	English
Journal	IEEE Transactions on Magnetics
Number of pages	5
ISSN	0018-9464
DOIs	https://doi.org/10.1109/TMAG.2025.3539977
Publication status	E-pub / Early view - 2025

Keywords

computational model
Hopfield oscillatory neural network (HONN)
magnetic vortex
Spin-torque vortex nano-oscillator (SVNO)

Access to Document

10.1109/TMAG.2025.3539977

Cite this

@article{309f7cc4107f495da289dbdbf3595999,

title = "A Neuromorphic Computational Model for Spintronics-based Hopfield Oscillatory Neural Network",

abstract = "The human brain is competent in information processing and learning, largely due to the coordinated activity of neuronal populations. These populations exhibit rhythmic fluctuations in activity known as oscillatory dynamics, observed across different brain regions. These oscillations are crucial in various cognitive functions, such as memory consolidation, sensory processing, and motor control. This work proposes a novel neuromorphic computational (NC) model comprising analytical derivation for a spintronics-based Hopfield oscillatory neural network (HONN) employing frequency synchronization inspired by the brain's oscillatory mechanism of pattern recognition and associative memory. Kuramoto model, which represents the phase-based coupling of two oscillators, this work presents an extended mathematical analysis (modeling) of frequency and phase-based dual coupling mechanism. Further, this model is translated to the Theile equation which governs the dynamics of magnetic vortex core (such as core position and oscillation frequency) applicable to spintronic-based HONN. This approach uses spin-torque vortex nano-oscillators (SVNOs) as neurons connected via resistive synapses representing synaptic coupling strength. The model describes the analytical relation between the SVNOs and the synaptic element, and how it influences the synchronized frequency (fsync). Stronger coupling aligns fsync closer to the higher gyrotropic frequency of the magnetic vortex core within the network, while weaker coupling promotes fsync closer to the lower one. The synaptic connections transition between low resistance (LRS) and high resistance (HRS) states mimicking biological brain plasticity. This NC model is then utilized to design a spintronic-based HONN circuit to illustrate oscillatory properties, frequency-based synchronization, and resistive coupling to create an energy-efficient and scalable architecture. The proposed NC model represents a promising approach to advancing large-scale HONN hardware architecture, particularly by enabling the integration of SVNOs as neurons, resistive memories as synapses, and conventional electronics as peripherals. This model serves as a foundational framework for exploring the feasibility, functionality, and reliability of advanced neural network architectures, crucial for evaluating the potential of these hybrid systems in practical, large-scale applications.",

keywords = "computational model, Hopfield oscillatory neural network (HONN), magnetic vortex, Spin-torque vortex nano-oscillator (SVNO)",

author = "Sandeep Soni and Yasser Rezaeiyan and Tim Boehnert and Ricardo Ferreira and Kaushik, {Brajesh Kumar} and Farshad Moradi and Sonal Shreya",

note = "Publisher Copyright: {\textcopyright} 2025 IEEE.",

year = "2025",

doi = "10.1109/TMAG.2025.3539977",

language = "English",

journal = "IEEE Transactions on Magnetics",

issn = "0018-9464",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - JOUR

T1 - A Neuromorphic Computational Model for Spintronics-based Hopfield Oscillatory Neural Network

AU - Soni, Sandeep

AU - Rezaeiyan, Yasser

AU - Boehnert, Tim

AU - Ferreira, Ricardo

AU - Kaushik, Brajesh Kumar

AU - Moradi, Farshad

AU - Shreya, Sonal

PY - 2025

Y1 - 2025

N2 - The human brain is competent in information processing and learning, largely due to the coordinated activity of neuronal populations. These populations exhibit rhythmic fluctuations in activity known as oscillatory dynamics, observed across different brain regions. These oscillations are crucial in various cognitive functions, such as memory consolidation, sensory processing, and motor control. This work proposes a novel neuromorphic computational (NC) model comprising analytical derivation for a spintronics-based Hopfield oscillatory neural network (HONN) employing frequency synchronization inspired by the brain's oscillatory mechanism of pattern recognition and associative memory. Kuramoto model, which represents the phase-based coupling of two oscillators, this work presents an extended mathematical analysis (modeling) of frequency and phase-based dual coupling mechanism. Further, this model is translated to the Theile equation which governs the dynamics of magnetic vortex core (such as core position and oscillation frequency) applicable to spintronic-based HONN. This approach uses spin-torque vortex nano-oscillators (SVNOs) as neurons connected via resistive synapses representing synaptic coupling strength. The model describes the analytical relation between the SVNOs and the synaptic element, and how it influences the synchronized frequency (fsync). Stronger coupling aligns fsync closer to the higher gyrotropic frequency of the magnetic vortex core within the network, while weaker coupling promotes fsync closer to the lower one. The synaptic connections transition between low resistance (LRS) and high resistance (HRS) states mimicking biological brain plasticity. This NC model is then utilized to design a spintronic-based HONN circuit to illustrate oscillatory properties, frequency-based synchronization, and resistive coupling to create an energy-efficient and scalable architecture. The proposed NC model represents a promising approach to advancing large-scale HONN hardware architecture, particularly by enabling the integration of SVNOs as neurons, resistive memories as synapses, and conventional electronics as peripherals. This model serves as a foundational framework for exploring the feasibility, functionality, and reliability of advanced neural network architectures, crucial for evaluating the potential of these hybrid systems in practical, large-scale applications.

AB - The human brain is competent in information processing and learning, largely due to the coordinated activity of neuronal populations. These populations exhibit rhythmic fluctuations in activity known as oscillatory dynamics, observed across different brain regions. These oscillations are crucial in various cognitive functions, such as memory consolidation, sensory processing, and motor control. This work proposes a novel neuromorphic computational (NC) model comprising analytical derivation for a spintronics-based Hopfield oscillatory neural network (HONN) employing frequency synchronization inspired by the brain's oscillatory mechanism of pattern recognition and associative memory. Kuramoto model, which represents the phase-based coupling of two oscillators, this work presents an extended mathematical analysis (modeling) of frequency and phase-based dual coupling mechanism. Further, this model is translated to the Theile equation which governs the dynamics of magnetic vortex core (such as core position and oscillation frequency) applicable to spintronic-based HONN. This approach uses spin-torque vortex nano-oscillators (SVNOs) as neurons connected via resistive synapses representing synaptic coupling strength. The model describes the analytical relation between the SVNOs and the synaptic element, and how it influences the synchronized frequency (fsync). Stronger coupling aligns fsync closer to the higher gyrotropic frequency of the magnetic vortex core within the network, while weaker coupling promotes fsync closer to the lower one. The synaptic connections transition between low resistance (LRS) and high resistance (HRS) states mimicking biological brain plasticity. This NC model is then utilized to design a spintronic-based HONN circuit to illustrate oscillatory properties, frequency-based synchronization, and resistive coupling to create an energy-efficient and scalable architecture. The proposed NC model represents a promising approach to advancing large-scale HONN hardware architecture, particularly by enabling the integration of SVNOs as neurons, resistive memories as synapses, and conventional electronics as peripherals. This model serves as a foundational framework for exploring the feasibility, functionality, and reliability of advanced neural network architectures, crucial for evaluating the potential of these hybrid systems in practical, large-scale applications.

KW - computational model

KW - Hopfield oscillatory neural network (HONN)

KW - magnetic vortex

KW - Spin-torque vortex nano-oscillator (SVNO)

UR - http://www.scopus.com/inward/record.url?scp=85217537283&partnerID=8YFLogxK

U2 - 10.1109/TMAG.2025.3539977

DO - 10.1109/TMAG.2025.3539977

M3 - Journal article

AN - SCOPUS:85217537283

SN - 0018-9464

JO - IEEE Transactions on Magnetics

JF - IEEE Transactions on Magnetics

ER -

A Neuromorphic Computational Model for Spintronics-based Hopfield Oscillatory Neural Network

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this