Frustration, glassy behavior and dynamical annealing in societies of Neural Networks

TL;DR

This paper models societal opinion dynamics using neural networks, revealing how surprise-driven learning leads to complex behaviors like polarization and glassy states depending on issue complexity.

Contribution

It introduces a maximum entropy framework for opinion exchange, incorporating surprise, distrust, and confidence, and analyzes resulting societal behaviors including frustration and dynamical annealing.

Findings

Societies reach polarized states for small issue sets.

Large issue sets lead to spin-glass-like long transient states.

Frustration arises from ideological and affective sources.

Abstract

We study maximum entropy mechanisms of information exchange between agents modeled by neural networks and the macroscopic states of a society of such agents in a few situations. Mathematical quantification of surprise, distrust of other agents and confidence about its opinion emerge as essential ingredients in the entropy based learning dynamics. Learning is shown to be driven by surprises, i.e. the receptor agent is confronted with the concurring opinion of a distrusted agent or with a trusted agent's disagreeing opinion. Attribution of blame for the surprise derives from measures of distrust of the receiver towards the emitter agent and the receiver's confidence about its own opinion. The dynamics proceeds by changes of mainly one or the other: the receptor opinion about the issue or the distrust about the emitter. A society with $N$ agents exchanging binary opinions about a set of issues show rich behavior which depend on the complexity of the agenda. For small sets the society reaches a steady state polarized into antagonistic factions, where balanced norms such as "the friend of an enemy is an enemy" are strictly satisfied. For larger sets of issues, societies can persist for a long time in spin-glass like states. There are two types of frustration: ideological and affective, with dynamical annealing properties depending on the complexity of the set of questions under discussion, leading to the lack of sharply defined parties for long transients.