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Emergent Collective Memory in Decentralized Multi-Agent AI Systems

Khushiyant

TL;DR

The paper addresses scalable coordination in decentralized AI by integrating four-category internal memories with four-category environmental traces in a grid-based agent framework. It develops a mathematical mean-field framework that predicts a critical density ρ_c ≈ 0.23 for a transition from memory-dominated to stigmergy-dominated coordination and validates this phase transition through extensive density-sweep experiments on grids up to 50×50. Key findings show that memory alone provides substantial coordination benefits, traces require memory to interpret, and at high densities traces outperform memory on composite metrics, despite lower food efficiency. The work offers practical guidance for designing density-aware decentralized systems and provides robust empirical validation of phase-transition-like behavior in collective cognition, with open-source data and code for reproducibility.

Abstract

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

Emergent Collective Memory in Decentralized Multi-Agent AI Systems

TL;DR

The paper addresses scalable coordination in decentralized AI by integrating four-category internal memories with four-category environmental traces in a grid-based agent framework. It develops a mathematical mean-field framework that predicts a critical density ρ_c ≈ 0.23 for a transition from memory-dominated to stigmergy-dominated coordination and validates this phase transition through extensive density-sweep experiments on grids up to 50×50. Key findings show that memory alone provides substantial coordination benefits, traces require memory to interpret, and at high densities traces outperform memory on composite metrics, despite lower food efficiency. The work offers practical guidance for designing density-aware decentralized systems and provides robust empirical validation of phase-transition-like behavior in collective cognition, with open-source data and code for reproducibility.

Abstract

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

Paper Structure

This paper contains 36 sections, 1 theorem, 29 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Methodology
  4. Agent-Based Model Architecture
  5. Environmental Trace System
  6. Mathematical Framework
  7. Overview: Modeling Collective Memory Emergence
  8. Formal Definitions
  9. Individual Memory Dynamics
  10. Environmental Trace Dynamics
  11. Mean-Field Theory and Phase Transitions
  12. Information Flow and System Metrics
  13. Experimental Design and Validation
  14. Baseline and Comparative Configurations
  15. Environment and Scenario Parameters
  16. ...and 21 more sections

Key Result

Theorem 1

There exists a critical agent density such that if $\rho < \rho_c$, individual memories predominate with weak collective behavior, while if $\rho > \rho_c$, a robust collective memory and coordinated behaviors arise. A derivation of $\rho_c$ using a linear stability analysis of the mean-field model is provided in Appendix sec:rho_c_deri

Figures (4)

  • Figure 1: Theoretical phase transition prediction showing order parameter (normalized coordination events: fraction of movements guided by consensus above threshold 1.2) evolution across density range. Theoretical critical density $\rho_c = 0.230$ (vertical line) marks the predicted transition point. While this figure shows theoretical mean-field predictions, experimental validation of the phase transition is presented in Table \ref{['tab:phase_transition']} using systematic density-sweep experiments spanning $\rho \in [0.049, 0.300]$ on grids up to 50×50 with 625 agents, confirming the predicted critical density within 13% error.
  • Figure 2: Temporal evolution of environmental trace strength over 100 simulation steps, demonstrating consensus formation (red hotspots) and decay patterns in a 25×25 grid with 10 agents.
  • Figure 3: Spatial heatmap of consensus strength showing areas of reinforced environmental trace agreement among agents, illustrating emergent collective memory hotspots.
  • Figure :

Theorems & Definitions (1)

  • Theorem 1: Phase Transition of Collective Memory