Modeling Systemic Contagion, Algorithmic Monoculture, and Collective Intelligence via Topological Deep Learning and Cyber-Physical Interfaces.

This repository hosts Horizon 3 of the Algoplexity Research Program. While Horizon 2 (The Reflective Physicist) solved the control problem for the individual agent (The Pilot), Horizon 3 builds "The Civic Nervous System": a fractal architecture that scales coherence from the local "Room" to the global "Model."

Hypothesis: Collective phenomena—whether financial crashes, social panics, or gridlocked policymaking—are Emergent Computations. They arise from the synchronization of Nested Optimization Processes across a network.

The Grand Synthesis: We model these systems by integrating three layers of theory:

1. The Physics (AID): We define "Structure" using Algorithmic Information Dynamics [Zenil et al.].
2. The Agent (UAI/QCEA): We define "Intelligence" as the struggle to maintain coherence against entropy [Hutter; Williams].
3. The Network (Higher-Order Cybernetics): We define "Consensus" as a Simplicial Phase Transition driven by simultaneous reinforcement [Battiston et al.].

The Diagnostic Threshold (Williams, 2025): We define "Systemic Failure" (e.g., Polarization or Market Collapse) as a Global Coherence Loss. This occurs when the Endogenous Environmental Drift ($\Lambda_{Hive}$)—driven by feedback loops—exceeds the Collective Update Rate ($\eta_{Hive}$) of the network's consensus mechanism.

$$ \Lambda_{Hive} > \eta_{Hive} \implies \text{Systemic Collapse (Rule 60)} $$

To model a "Hive Mind" capable of stewarding collective intelligence, we integrate three state-of-the-art frameworks:

• The Limit: Standard GNNs assume static node logic. They cannot model human agents that learn or panic in real-time.
• The Solution: We replace the standard MLP update rule with a Self-Modifying Titan Architecture [Behrouz et al., 2025] utilizing Global Self-Attention [Tesfaldet et al., 2022].
  • Fast Weights: The "Reflex" (System 1) that adapts to immediate neighbor pressure (e.g., Panic Selling / Mob Mentality).
  • Slow Weights: The "Strategy" (System 2) that evolves over long horizons (e.g., Cultural Norms).
  • Result: The network is not just a CA; it is a Distributed Deep Optimizer.

• The Insight (Battiston, 2025): "Higher-order interactions drive collective human behavior." Linear links ($A \to B$) are insufficient for complex contagion.
• The Solution: We upgrade the graph from Edges to Simplices (Triangles/Tetrahedrons).
  • The Simultaneity Gate: The GNCA update rule includes a non-linear term that triggers only when neighbors interact simultaneously. This mathematically models the "Room" dynamics where consensus requires reinforcement, not just connection.

• The Insight (Brookings, 2025): "Rooms lack live maps; maps lack street addresses." We need infrastructure to bridge the "Design-Minded" (Facilitators) and "Model-Minded" (System Dynamicists).
• The Solution: A Cyber-Physical System (CPS) implementation of the GNCA.
  • Input: Multi-modal sensors (Audio/Capacitive) detect local interaction topology.
  • Processing: An Edge-GNCA (running on ESP32) calculates the local entropy.
  • Feedback: Ambient Haptics/Light allow the group to "feel" their own coherence.

This repository bridges the gap between theoretical specifications, executable PyTorch implementations, and hardware firmware.

├── docs/
│   └── specs/                 
│       ├── 01_Financial_Boids_Spec.md  # Spec for Market Herds
│       └── 02_Civic_Nervous_System.md  # Spec for the "Room+Model" Architecture
├── modules/
│   ├── gnca_titan.py          # The Core Engine: Deep Learning CA
│   ├── simplicial_layer.py    # The Battiston Topology: Detecting Triangles
│   └── diff_logic.py          # Differentiable Logic Gates for rule extraction
├── hardware/                  # THE CIVIC RESONATOR (CPS)
│   ├── firmware/              # ESP32 C++ code for GNCA Edge Logic
│   ├── cad/                   # 3D Print files for the "Stone" chassis
│   └── schematics/            # Wiring for Capacitive/Audio Arrays
├── notebooks/                 
│   ├── 00_Scout_Delta_Topology.ipynb   # Exp 0: Identifying latent communities
│   ├── 02_Continuous_Herding.ipynb     # Exp 2: The Physics of Panic
│   └── 04_Nelson_Wetlands_Sim.ipynb    # Exp 3: The "Green Energy" Conflict Simulation
├── results/                   
│   ├── Figure_6_Hive_Mind_Entropy.png  # Visualizing the "Entropy of Thought"
│   └── Figure_8_Simplicial_Bloom.png   # Visualizing Consensus Percolation
└── requirements.txt           

• Objective: Validate that a latent graph exists in high-dimensional agent data.
• Method: Applied "Delta Scout" protocol to single-cell perturbation data.
• Result: Confirmed. Identified distinct communities (Clustering Coeff: 0.36) and rejected the "Hairball" null hypothesis. The "Hive Mind" has structure.

• Objective: Prove that Higher-Order Interactions are required for consensus.
• Method: Compare Standard GNCA vs. Simplicial GNCA on a polarization task.
• Result: Standard GNCA gets stuck in "Local Minima" (Polarization). Simplicial GNCA achieves Global Coherence 40% faster by "bridging" clusters via triangles.

• Objective: Modeling Algorithmic Monoculture.
• Discovery: The GNCA learned to simulate the herd autonomously. Entropic Collapse (Figure 6) precedes the crash, linking Horizon 3 back to the Horizon 1 "Somatic Marker."

• Context: Based on the Nelson Wetlands (ABC, 2025) case study.
• Objective: Simulate a conflict between "Global Optimization" (Wind Developer) and "Local Topology" (Ecologist/Community).
• The Simulation: A "Room + Model" setup where 4 GNCA agents with conflicting objective functions interact via a Civic Resonator.
• Result: Without the Resonator, the system oscillates between Rule 54 (Gridlock) and Rule 60 (Backlash). With the Resonator (Haptic Feedback), the system finds a Renormalized State (Rule 110) that satisfies local constraints while meeting global targets.

• Target: Meeting the Brookings Institution mandate for "AI that changes the physics of collective intelligence."
• Mechanism: Renormalization. Connecting "Local Resonators" (Town Halls) into a global graph. This allows "Smart Local Actions" to scale without being lost in the noise of the global model.

• Target: Validating the "Flash Crash" mechanism for UCL/EPSRC Project ID 2531bd1646.
• Mechanism: Modeling Lyapunov Synchronization. A crash occurs when agents synchronize on a "Chaos Prior" (Panic), causing the effective Lyapunov exponent to spike ($\lambda_{Hive} > 0$).

• Target: Providing the "Systemic Dashboard" for ANU School of Cybernetics.
• Mechanism: Detecting Groupthink (Low Entropy) before it leads to strategic failure, allowing leaders to inject "Requisite Variety" (Ashby's Law).

This research program is built on a cumulative stack of theoretical physics, artificial intelligence, and network science.

The Physics of Intelligence and Complexity.

1. Hutter, M. (2005). Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability. Springer. (The Mathematical Foundation of General Intelligence).
2. Zenil, H., & Delahaye, J. P. (2010). An algorithmic information-theoretic approach to the behaviour of financial markets. arXiv:1008.1846. (The Physics of Causal Structure).
3. Williams, C. F. (2025). Strategy as Ontology: A Quantum–Complex–Entropic–Adaptive Framework. SSRN. (The Thermodynamics of Viability).
4. Mak, Y. W. (2025a). The Coherence Meter: A Hybrid AIT-MDL Framework for Early-Warning Structural Break Detection. (Horizon 1 Outcome).
5. Mak, Y. W. (2025b). The Computational Phase Transition: Quantifying the Algorithmic Information Dynamics of Financial Crises. (Horizon 1 Outcome).

The Architecture of the Hive Mind.

6. Behrouz, A., et al. (2025). Nested Learning: The Illusion of Deep Learning Architectures. NeurIPS 2025. (The Titan Architecture / Fast-Slow Weights).
7. Grattarola, D., Livi, L., & Alippi, C. (2021). Learning Graph Cellular Automata. NeurIPS 2021. (The GNCA Engine).
8. Tesfaldet, M., et al. (2022). Attention-based Neural Cellular Automata. NeurIPS 2022. (The Global Attention Mechanism).

The Mandate for Cyber-Physical Stewardship.

9. Battiston, F., et al. (2025). Higher-order interactions drive collective human behavior. Nature Human Behaviour. (The Simplicial Topology).
10. Taylor, J. (2025). It’s time for collective intelligence. Brookings Institution. (The "Room vs. Model" Problem Statement).
11. ABC News. (2025). Nelson Wetlands green energy boom planning protections. (The "Case Zero" for the Civic Resonator).

If you utilize the Algoplexity framework, please cite the program root:

@misc{algoplexity_program,
  author = {Mak, Yeu Wen},
  title = {The Algoplexity Research Program: Foundations of Algorithmic Cognitive Systems},
  year = {2025},
  publisher = {GitHub},
  journal = {GitHub repository},
  howpublished = {\url{https://github.com/algoplexity/algoplexity}}
}