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The recurrent Hopfield mass model: Scalability and optimization.

Martina Ferrazza1, Giorgio Gosti2, Edoardo Milanetti3

  • 1International School of Advanced Studies, University of Camerino, Camerino, Italy; DNISC and ITAB, 'G. D'Annunzio' University of Chieti-Pescara, Chieti, Italy; Center for Life Nano- and Neuro-Science, Istituto Italiano di Tecnologia, Rome, Italy.

Neural Networks : the Official Journal of the International Neural Network Society
|December 11, 2025
PubMed
Summary
This summary is machine-generated.

The Recurrent Hopfield Mass Model (RHoMM) effectively estimates brain connectivity from MEG data. Optimizing RHoMM without normalization improves scalability and accuracy for large-scale network analysis.

Keywords:
Effective connectivityHopfield networkHyperparameters searchMagnetoencephalographyRecurrent neural networks

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Area of Science:

  • Computational neuroscience
  • Brain imaging analysis
  • Network modeling

Background:

  • Magnetoencephalography (MEG) provides high temporal resolution for studying brain activity.
  • Estimating large-scale effective connectivity is crucial for understanding brain function.
  • Existing generative models face challenges in scalability and data-driven application.

Purpose of the Study:

  • To evaluate the scalability of the Recurrent Hopfield Mass Model (RHoMM).
  • To optimize RHoMM performance across various network sizes (20-200 nodes).
  • To assess the impact of training parameters on RHoMM accuracy.

Main Methods:

  • Utilized simulated networks with diverse architectures to test RHoMM.
  • Investigated the effects of L1 normalization and bias addition during training.
  • Validated the model using experimental MEG data from 10 subjects (155-node network).

Main Results:

  • RHoMM without L1 normalization demonstrated wider learning rate intervals and faster convergence.
  • Reduced inference errors in effective connectivity matrices were observed without normalization.
  • Model performance was independent of objective network architecture.
  • Successful validation on experimental MEG data confirmed scalability.

Conclusions:

  • RHoMM is a scalable, data-driven generative model for effective connectivity estimation.
  • Omitting L1 normalization enhances RHoMM's scalability and performance.
  • The model shows promise for analyzing standard-size human connectomes from MEG data.