Graphon Signal Processing for Spiking and Biological Neural Networks

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.