The Stochastic Complexity of Spin Models: Are Pairwise Models Really Simple?

Area of Science:

• Statistical physics
• Information theory
• Computational complexity

Background:

• Model simplicity is crucial for interpretation and prediction.
• Stochastic complexity quantifies model simplicity in information theory.
• Spin models are used to study complex systems.

Purpose of the Study:

• To investigate the factors determining model simplicity in spin models.
• To understand how interaction structure influences stochastic complexity.
• To identify characteristics of simple and complex models.

Main Methods:

• Studied stochastic complexity of spin models with arbitrary order interactions.
• Utilized bijections within interaction spaces to identify equivalence classes.
• Analyzed the relationship between interaction arrangements and model complexity.

Main Results:

• Model simplicity is determined by the arrangement, not the order, of interactions.
• Localized, non-overlapping interactions lead to simple models.
• Fully connected pairwise models exhibit high complexity.

Conclusions:

• Simple models possess localized dependencies and yield falsifiable predictions.
• Complex models, like fully connected pairwise models, are difficult to falsify.
• Understanding interaction arrangements is key to designing simple, predictive models.