Diverse Mean-Field Dynamics of Clustered, Inhibition-Stabilized Hawkes Networks via Combinatorial Threshold-Linear Networks
Name
m8hf-q5pl.pdf
Size
5.59 MB
Format
Adobe PDF
Checksum (MD5)
3ad1137507f750e86488e907369bf5a9
Author(s)
Lienkaemper, Caitlin
Koch Ocker, Gabriel
Date Issued
October 14, 2025
Journal
PRX Life
Publisher
American Physical Society
Version
Final published version
Abstract
Networks of interconnected neurons display diverse patterns of collective activity. Relating this collective activity to the network's connectivity structure is a key goal of computational neuroscience. We approach this question for clustered networks, which can form via biologically realistic learning rules and allow for the reactivation of learned patterns. Previous studies of clustered networks have focused on metastabilty between fixed points, leaving open the question of whether clustered spiking networks can display richer dynamics-and if so, whether these can be predicted from their connectivity. Here we show that in the limits of large population size and fast inhibition, the combinatorial threshold linear network (CTLN) model is a mean-field theory for inhibition-stabilized nonlinear Hawkes networks with clustered connectivity. The CTLN has a large body of "graph rules" relating network structure to dynamics. By applying these, we can predict the dynamic attractors of our clustered spiking networks from the structure of between-cluster connectivity. This allows us to construct networks displaying a diverse array of nonlinear cluster dynamics, including metastable periodic orbits and chaotic attractors. Relaxing the assumption that inhibition is fast, we see that the CTLN model is still able to predict the activity of clustered spiking networks with reasonable inhibitory timescales. For slow enough inhibition, we observe bifurcations between CTLN-like dynamics and global excitatory/inhibitory oscillations.
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/m8hf-q5pl
