Dynamical and Coupling Structure of Pulse-Coupled Networks in Maximum Entropy Analysis

TL;DR

This paper explores the relationship between the dynamical effective interactions identified by maximum entropy analysis and the actual coupling structure of pulse-coupled networks, revealing how sparse coupling can lead to sparse coding.

Contribution

It establishes a quantitative relation between the network's coupling structure and the effective interactions in maximum entropy analysis, enhancing understanding of neural coding mechanisms.

Findings

Effective interactions reflect the network's coupling structure.

Sparse coupling leads to sparse effective interactions.

The relation helps interpret neural dynamics in terms of network structure.

Abstract

Maximum entropy principle (MEP) analysis with few non-zero effective interactions successfully characterizes the distribution of dynamical states of pulse-coupled networks in many experiments, e.g., in neuroscience. To better understand the underlying mechanism, we found a relation between the dynamical structure, i.e., effective interactions in MEP analysis, and the coupling structure of pulse-coupled network to understand how a sparse coupling structure could lead to a sparse coding by effective interactions. This relation quantitatively displays how the dynamical structure is closely related to the coupling structure.