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A Categorical Framework for Quantifying Emergent Effects in Network Topology.
Johnny Jingze Li1, Sebastian Pardo Guerra2, Kalyan Basu3
1Center for Engineered Natural Intelligence and Department of Mathematics, University of California San Diego, La Jolla, CA 92093, U.S.A. jil164@ucsd.edu.
Neural Computation
|July 8, 2025
Summary
We introduce a new framework using homological algebra to measure emergent effects in complex systems. This approach links system properties to network structure, enabling prediction and understanding of emergence.
Area of Science:
- Complex Systems Science
- Network Theory
- Computational Mathematics
Background:
- Emergent effects are key to complex systems but lack theoretical measurement frameworks.
- Understanding emergence requires quantifying properties not present in individual components.
Purpose of the Study:
- To develop a computational measure for quantifying emergent effects in complex systems.
- To establish a theoretical framework linking emergence to network topology and structure.
Main Methods:
- Utilizing homological algebra to model emergence as structural nonlinearity.
- Encoding emergence within the mathematical structure of cohomologies.
- Applying the framework to network models for computational measurement.
Main Results:
- Developed a novel computational measure of emergence based on network topology.
- Demonstrated that the measure correlates with existing information-theoretic measures.
- Showcased the framework's ability to predict and explain emergent effects.
Conclusions:
- The proposed framework provides a robust method for measuring and understanding emergence.
- Network topology and local structures are critical determinants of emergent potential.
- This work offers a pathway to predict and analyze emergent phenomena in diverse complex systems.
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