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Graphon Signal Processing for Spiking and Biological Neural Networks.

Takuma Sumi1, Georgi S Medvedev2

  • 1Hotchkiss Brain Institute, Cumming School of Medicine, University of Calgary, Calgary, Alberta T2N 1N4, Canada takuma.sumi@ucalgary.ca.

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Graphon signal processing (GnSP) enhances network data analysis by providing stable, efficient methods for large networks. This study applies GnSP to neural networks, improving stimulus identification and creating robust data embeddings.

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Area of Science:

  • Computational neuroscience
  • Network science
  • Signal processing

Background:

  • Graph signal processing (GSP) analyzes network data, but can be sensitive to variability.
  • Graphon signal processing (GnSP) uses graphon theory for more stable and efficient GSP, especially for large networks.

Purpose of the Study:

  • To apply GnSP to the stimulus identification problem (SIP) in computational and biological neural networks.
  • To evaluate the performance of GnSP-based methods against existing techniques like PCA and discrete GSP.

Main Methods:

  • Utilized graphon theory to develop GnSP methods for analyzing neural network data.
  • Applied these methods to simulated spiking neural networks and experimental calcium imaging recordings.
  • Employed graphon-based spectral projections for data embedding and stimulus classification.

Main Results:

  • Graphon-based spectral projections created trial-invariant, low-dimensional embeddings.
  • These embeddings significantly improved stimulus classification compared to PCA and discrete GSP.
  • The embeddings demonstrated robustness to network size variations and noise levels.

Conclusions:

  • GnSP offers a stable and efficient framework for analyzing neural network data, outperforming traditional methods.
  • This work represents the first application of GnSP to biological neural networks, opening new research avenues.
  • Graphon-based analysis shows promise for understanding neural coding and network dynamics in neuroscience.