Bringing Collective Intelligence to Graph Pathfinding
Can we bring collective intelligence into computational navigation—where systems learn from experience instead of starting from zero every time?
STAN (Stigmergic A Navigation)* is a novel graph pathfinding system that combines classical A* algorithms with stigmergic coordination principles inspired by ant colony optimization. Just as ant colonies discover optimal paths through pheromone trails, STAN creates a system that improves the more it's used.
This repository contains our research paper and demonstration materials exploring this approach.
Our research demonstrates that stigmergic principles successfully operate in computational graph spaces:
- 95% cost reduction within 10 iterations using stigmergic feedback loops
- Power-law pheromone patterns emerge naturally, similar to natural ant trails
- Emergent "super-highways" in the graph discovered through repeated exploration—not explicitly programmed
- Real-time performance (<100ms queries) with production-ready implementation
- Comprehensive validation through 40,000+ route tests and 10+ hours of continuous operation
The most interesting part? Simple local rules led to complex patterns—a reminder that sometimes intelligence comes from coordination, not complexity.
Traditional pathfinding algorithms (Dijkstra, A*) find optimal paths but don't learn from experience. Each query starts from scratch. STAN changes this by introducing pheromone-weighted edge costs:
cost_effective = base_weight / (1 + pheromone × influence)
The feedback loop:
- Agents navigate the graph using modified A*
- Successful paths receive pheromone deposits
- High-pheromone edges become cheaper to traverse
- More agents use these paths, reinforcing them further
- Pheromones gradually evaporate, allowing adaptation
Without explicit programming, STAN discovers:
- Conceptual hierarchies: Certain nodes become dominant hubs through collective validation
- Super-highway edges: 0.4% of edges accumulate 94.9% of all pheromones (power-law distribution)
- Bridge concepts: Nodes that serve as critical connectors between different regions
- Collective optimization: 49.53% mean cost reduction across diverse navigation scenarios
| Metric | Result | Significance |
|---|---|---|
| Cost reduction | 95.0% | Matches classical ACO performance (90-98%) |
| Convergence speed | 10 iterations | Rapid optimization comparable to ant colonies |
| Routes tested | 40,000+ | Statistical significance validated |
| Continuous operation | 10+ hours | Long-term stability demonstrated |
| Query latency | <100ms | Production-ready performance |
| Pheromone distribution | Zipfian (power-law) | Natural stigmergic patterns reproduced |
| Algorithm | Cost Reduction | Adaptation | Learning | Real-time |
|---|---|---|---|---|
| Dijkstra | 0% | None | None | Yes |
| A* | 0% | None | None | Yes |
| PageRank | N/A | None | Implicit | Yes |
| Classical ACO | 90-98% | Batch only | Batch only | No |
| STAN | 95% | Continuous | Explicit | Yes |
STAN's unique contribution: Persistent pheromones in a graph database enable continuous learning across system restarts—bridging the gap between classical optimization and production systems.
STAN_Research_Paper_Dey_2025.pdf
Full academic paper including:
- Theoretical foundations and algorithm design
- Comprehensive experimental methodology
- Statistical validation (bootstrap CI, Monte Carlo, power analysis)
- Comparison to classical ACO variants (AS, MMAS, ACS)
- Discussion of admissibility trade-offs
- Applications to AI reasoning, recommendation systems, decentralized decision-making
Abstract excerpt:
Through comprehensive empirical analysis of 40,000+ routes and 10+ hours of continuous operation, we demonstrate that STAN achieves 95% cost reduction through pheromone-based collective optimization, with pheromone distributions following power-law patterns observed in natural systems.
Visual demonstration of STAN's pheromone evolution and pathfinding in action.
STAN is production-ready with:
- Database: Memgraph 2.x (persistent pheromone storage)
- API: FastAPI with REST endpoints
- AI Integration: MCP (Model Context Protocol) server with 9 tools
- Deployment: Docker Compose, Kubernetes manifests
- Testing: 100% test pass rate (9/9 unit tests)
Architecture:
Application Layer: REST API | MCP Server | WebSocket Interface
↓
Service Layer: Pathfinding | Pattern Mining | Analytics
↓
Data Layer: Memgraph Graph Database (185 nodes, 3,570 edges)
STAN enables novel approaches to:
- LLMs traversing knowledge graphs 20× faster through collective experience
- Multi-agent reasoning with shared pheromone memory
- Self-organizing content pathways validated by user behavior
- Auto-adaptation via pheromone decay as preferences shift
- Swarm robotics without central control
- Distributed computing load balancing
- Blockchain consensus protocols
- Automatic discovery of canonical literature paths
- Citation graph exploration with collective validation
"TEMPORAL ORDERINGS I became the dominant conceptual hub (average 76.58 pheromone/edge) without explicit programming. This pattern arose from 155,700 explorations and may reflect either graph topology, rich-get-richer dynamics, or genuine conceptual centrality."
The emergence is genuine (not programmed), but its interpretation remains ambiguous—a reminder that what systems "discover" may reflect the environment's structure as much as underlying truth.
"Intelligence may be less about individual capability and more about effective coordination. A thousand simple agents with stigmergic coordination can discover what a single sophisticated agent cannot."
STAN validates key concepts from the Hyperseed-1 AGI ontology:
- Emergence: Collective optimization (84% score) far exceeds individual intelligence
- Tendency to Take Habits: Stigmergic feedback demonstrates experience-based learning
- Intersubjective Reality: Pheromone graph as collective knowledge representation
- Morphic Resonance: High-pheromone routes create spatial influence fields
If you use STAN in your research, please cite:
@article{dey2025stan,
title={STAN: Stigmergic A* Navigation for Emergent Intelligence in Graph Pathfinding},
author={Dey, Robin},
journal={Vicharatmak Buddhi Research Labs},
year={2025},
month={December},
url={https://github.com/vbrltech/STAN}
}Plain text:
Dey, R. (2025). STAN: Stigmergic A* Navigation for Emergent Intelligence
in Graph Pathfinding. Vicharatmak Buddhi Research Labs (VBRL.ai).
https://github.com/vbrltech/STAN
Robin Dey Founder, VBRL.ai (Vicharatmak Buddhi Research Labs) 📧 robin@vbrl.ai
This work investigates whether stigmergic principles—proven in biological systems—can be successfully applied to computational graph navigation. By demonstrating 95% cost reduction comparable to classical ant colony optimization results, we provide evidence that:
- Stigmergy works in abstract computational spaces, not just physical environments
- Simple local rules can produce complex optimization patterns without central control
- Production systems can benefit from bio-inspired collective intelligence while maintaining real-time performance
- Emergent behavior in AI systems may be achievable through coordination mechanisms rather than architectural complexity
This research builds on foundational work in:
- Ant Colony Optimization (Dorigo, 1992): Original ACO algorithms for TSP
- Stigmergy (Grassé, 1959): Theory of indirect coordination in social insects
- Swarm Intelligence (Bonabeau et al., 1999): Collective behavior in natural and artificial systems
- Graph Pathfinding (Dijkstra, 1959; Hart et al., 1968): Classical algorithms for shortest paths
- Hyperseed-1 Ontology (Goertzel, 2024): AGI-oriented conceptual frameworks
- Tested on 185-node graph; scalability to 100,000+ nodes requires validation
- Single knowledge graph dataset (Hyperseed-1); generalization needs diverse graphs
- No adversarial testing (cooperative vs. competitive environments)
- Coherence remains low (high variance) during exploration phase
- Multi-timeframe stigmergy: Agents operating at different temporal scales
- Hybrid approaches: Combining pheromones with neural embeddings
- Adaptive decay models: Context-sensitive evaporation rates
- Meta-stigmergy: Pheromones on pheromones for learning to learn
Does TEMPORAL ORDERINGS I's dominance reflect:
- Graph topology (degree centrality, structural advantage)?
- Rich-get-richer dynamics (preferential attachment)?
- Genuine conceptual centrality in AGI reasoning?
Further experiments with randomized graph topologies are needed to distinguish structural artifacts from genuine discovery.
This research is released under the MIT License—free to use, modify, and distribute with attribution.
MIT License
Copyright (c) 2025 Robin Dey, VBRL.ai
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
- 🌐 Website: vbrl.ai
- 📧 Email: robin@vbrl.ai
- 💬 Discussions: GitHub Discussions
- 🐛 Issues: GitHub Issues
"Stigmergy works in ant colonies. It works in knowledge graphs. Whether it scales to artificial general intelligence remains an open empirical question."
⭐ Star this repository if you find this research interesting! ⭐