Self-organizing graph reasoning evolves into a critical state for continuous discovery through structural-semantic...

Area of Science:

• Complex Systems Science
• Artificial Intelligence
• Information Theory

Background:

• Agentic graph reasoning systems are crucial for AI, but understanding their emergent properties is challenging.
• Complex systems often exhibit self-organized criticality, a state conducive to adaptation and innovation.

Purpose of the Study:

• To investigate the emergent dynamics of agentic graph reasoning systems.
• To identify the principles governing continuous semantic discovery and adaptation.
• To establish parallels between these systems and critical phenomena in other complex systems.

Main Methods:

• Analysis of structural (Von Neumann graph entropy) and semantic (embedding) entropy.
• Quantification using a dimensionless critical discovery parameter.
• Empirical observation of edge properties and topological features (scale-free, small-world).

Main Results:

• A critical regime was identified where semantic entropy consistently dominates structural entropy.
• A stable fraction of "surprising" edges (12%) indicates long-range semantic connections.
• The system exhibits scale-free, small-world topology and negative cross-correlation between structural and semantic measures, akin to self-organized criticality.

Conclusions:

• Agentic graph reasoning systems spontaneously evolve toward a critical state supporting continuous semantic discovery.
• Semantic richness, not explicit programming, drives sustained exploration and adaptation.
• Findings offer insights for engineering adaptable AI and optimizing model training strategies for discovery.