Algorithmic Collective: A General Model for Swarm Intelligence

Abstract

The mechanisms underlying swarm intelligence remain largely unexplained theoretically, and existing frameworks struggle to account for both homogeneous and heterogeneous intelligent groups—this is the core problem addressed in this paper. Understanding how collective intelligence emerges from individual interactions is not only a theoretical gap in swarm intelligence research but also a critical issue in systems science, artificial intelligence, and human-machine collaboration. Based on complex adaptive systems theory and integrated with a generalized view of algorithms, this paper proposes the "algorithmic collective" model, whose theoretical innovations are threefold. First, it establishes three core ideas of the algorithmic perspective: the generalized algorithm expands the traditional scope of algorithms beyond computer programs to general rule systems; the unity of entity and rule holds that an algorithmic unit is both an objective entity and a process of rule execution, the two being dialectically unified; the hierarchy of entity and rule reveals the nested relationship between macro-rules and micro-rules, providing methodological guidance for cross-level modeling. Second, it defines the "algorithmic unit" as the basic rule-system individual constituting a group, replacing the concept of adaptive agent, with four advantages: thorough monism, wide applicability, explicit representation of heterogeneity, and higher operability. Third, it constructs a three-layer conceptual model consisting of the entity layer, rule layer, and function layer, forming a closed-loop evolutionary path of institutionalization, emergence, and embodiment. The rule layer is further decomposed into three parallel sub-rules: individual rules, communication rules, and leadership rules, decomposing the nonlinear interactions in swarm intelligence into designable, controllable, and measurable components. This study demonstrates that the algorithmic collective model provides a new ontological foundation and methodological tool for understanding the emergence process of swarm intelligence, and can effectively support computational modeling of swarm intelligence, analysis of heterogeneous groups, and interdisciplinary research on complex adaptive systems.