Knowledge Graph Topological Data Analysis

Originally validated: April 2, 2025
Author: Justin K. Lietz
Neuroca, Inc

Note: These frameworks represent the foundational validation work. Subsequent private testing has led to substantial improvements and additional discoveries including self-organization and self-repair mechanisms, unified integration of SNNs with SIE and Knowledge Graph TDA findings, and the development of Resonance Enhanced Valence Gated Synaptic Plasticity (REVGSP).

What This Does

Analyzes neural network "shape" to discover mathematical relationships about network health. Uses topology (the study of shape) to predict when networks will work well or break down.

Quick Start

From main project:

python main.py --kgtda

Direct run:

cd Implementation
python run_analysis.py

Discoveries

Finding 1: Complexity-Efficiency Trade-off

Correlation: r = -0.85, p = 0.002

Meaning: More complex network shapes → lower efficiency
Impact: There's an optimal complexity level for peak performance

Finding 2: Fragmentation-Pathology Relationship

Correlation: r = 0.997, p < 1e-9

Meaning: Broken/fragmented networks → high dysfunction
Impact: Network connectivity directly predicts health

Understanding Results

Healthy Network Indicators:

Components: 1 (fully connected)
B1 Persistence: 50-70 (moderate complexity)
Efficiency: >0.85 (good performance)
Pathology: <0.15 (low dysfunction)

Warning Signs:

Fragmentation: >5 components (network breakdown)
Over-complexity: B1 persistence >200 (too complex)
High pathology: >0.4 (serious dysfunction)

Example Results

Network Type	Components	B1 Persistence	Efficiency	Pathology	Status
Healthy	1	56	0.886	0.100	✅ Good
Efficient	2	0	0.900	0.100	✅ Good
Complex	1	230	0.835	0.100	⚠️ Slow
Fragmented	16	0	0.900	0.800	❌ Broken

Performance

Speed: ~0.07 seconds per 100-node network
Scales: Up to 500+ node networks efficiently
Accuracy: High statistical significance (p < 0.003)

Output Files

Results saved to results/:

tda_analysis_results.txt - Complete analysis with correlations
Individual snapshot analysis files
Network visualization plots

Possible Use Cases

This topology analysis framework could substantially improve:

AI Safety & System Health

Neural network monitoring for large language models and AI systems
Early warning detection for model degradation before failure
Quality assurance for AI systems in critical applications

Brain & Medical Research

Neurological disorder detection through brain connectivity analysis
Treatment monitoring via network topology changes over time
Neural implant optimization using topology-guided design principles

Social Network Analysis

Community health assessment in online platforms and social networks
Information flow optimization in organizational communication networks
Network resilience evaluation for distributed systems

Infrastructure Monitoring

Power grid stability assessment using topological health metrics
Communication network optimization through connectivity analysis
Supply chain resilience evaluation via fragmentation detection

Scientific Research

Protein interaction networks in drug discovery and biology
Ecosystem stability analysis through species interaction patterns
Materials science for optimizing molecular network structures

Dependencies

pip install numpy scipy networkx ripser matplotlib

Scientific Impact

Provides the first quantitative framework for predicting neural network health from topology, enabling real-time monitoring and design optimization.

License

This research is protected under a proprietary license. Use requires written permission from Justin K. Lietz. See ../LICENSE for full terms.