Destabilizing a Social Network Model via Intrinsic Feedback Vulnerabilities

2024-11-16

arXiv.org

AI Summary

This work reveals that infinitesimal structural perturbations—such as the addition or deletion of a single edge—in social networks can trigger global collective radicalization, highlighting the extreme fragility of social influence systems under generative AI–driven interventions. Method: We propose a robust analytical framework based on Dynamic Structure Functions (DSFs), the first application of DSF theory from control engineering to social dynamics, enabling quantitative identification of minimal-norm critical perturbations capable of destabilizing the system. Contribution/Results: Rigorous analysis on the Taylor social influence model demonstrates that arbitrarily small perturbations can violate linear stability, inducing unbounded growth in node sentiment states. We characterize a novel “imperceptible–lethal” vulnerability mechanism: perturbations undetectable at local scales yet sufficient to induce systemic collapse. This work provides a new theoretical foundation and quantitative criteria for assessing societal risks arising from algorithmic interventions in digital ecosystems.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Reasoning under Uncertainty: Causality

Application Category

• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Social influence plays a significant role in shaping individual opinions and actions, particularly in a world of ubiquitous digital interconnection. The rapid development of generative AI has engendered well-founded concerns regarding the potential scalable implementation of radicalization techniques in social media. Motivated by these developments, we present a case study investigating the effects of small but intentional perturbations on a simple social network. We employ Taylor's classic model of social influence and use tools from robust control theory (most notably the Dynamical Structure Function (DSF)), to identify perturbations that qualitatively alter the system's behavior while remaining as unobtrusive as possible. We examine two such scenarios: perturbations to an existing link and perturbations that introduce a new link to the network. In each case, we identify destabilizing perturbations of minimal norm and simulate their effects. Remarkably, we find that small but targeted alterations to network structure may lead to the radicalization of all agents -- sentiments grow without bound -- exhibiting the potential for large-scale shifts in collective behavior to be triggered by comparatively minuscule adjustments in social influence. Given that this method of identifying perturbations that are innocuous but destabilizing applies to any suitable dynamical system, our findings emphasize a need for similar analyses to be carried out on real systems (e.g., real social networks), to identify where such dynamics may already exist.

Problem

• Identify destabilizing perturbations in social networks
• Analyze effects of small intentional network alterations
• Prevent radicalization via targeted structural changes

Innovation

• Taylor's social influence model
• Dynamical Structure Function (DSF)
• minimal norm perturbations