Less is different: why sparse networks with inhibition differ from complete graphs

TL;DR

This paper demonstrates that in sparse neuronal networks, inhibition does not control phase transitions, contrasting with complete graph models, and highlights the importance of network topology in neuronal dynamics and computational flexibility.

Contribution

The study reveals that inhibition is not a control parameter in sparse networks, challenging previous models based on complete graphs, and explains the topology-dependent role of inhibition.

Findings

Inhibition does not govern phase transitions in sparse networks.

Network topology influences the role of inhibition in neuronal dynamics.

Sparse networks can maintain criticality while adjusting inhibitory weights for computation.

Abstract

In neuronal systems, inhibition contributes to stabilizing dynamics and regulating pattern formation. Through developing mean field theories of neuronal models, using complete graph networks, inhibition is commonly viewed as one ``control parameter'' of the system, promoting an absorbing phase transition. Here, we show that for low connectivity sparse networks, inhibition weight is not a control parameter of the transition. We present analytical and simulation results using generic stochastic integrate-and-fire neurons that, under specific restrictions, become other simpler stochastic neuron models common in literature, which allow us to show that our results are valid for those models as well. We also give a simple explanation about why the inhibition role depends on topology, even when the topology has a dimensionality greater than the critical one. The absorbing transition independence of the inhibitory weight may be an important feature of a sparse network, as it will allow the network to maintain a near-critical regime, self-tuning average excitation, but at the same time, have the freedom to adjust inhibitory weights for computation, learning, and memory, exploiting the benefits of criticality.