Statistical Physics through the Lens of Real-Space Mutual Information.

Area of Science:

• * Physics
• * Computational Science
• * Machine Learning

Background:

• * Identifying critical components (degrees of freedom) is crucial for developing physical theories.
• * Renormalization group methods offer a framework but require ad hoc choices in new systems.
• * Current machine learning (ML) approaches lack formal interpretability for these tasks.

Purpose of the Study:

• * To develop a new, interpretable ML-based paradigm for identifying relevant degrees of freedom.
• * To overcome the limitations of existing methods in complex physical systems.
• * To advance automated theory building in physics.

Main Methods:

• * Algorithm development leveraging state-of-the-art ML for information-theoretic quantity estimation.
• * Application to an interacting physical model to identify emergent degrees of freedom.
• * Focus on formal interpretability in ML applications.

Main Results:

• * Demonstrated a novel algorithm for identifying relevant operators in a physical system.
• * Showcased emergent degrees of freedom qualitatively distinct from microscopic constituents.
• * Achieved formally interpretable ML applications.

Conclusions:

• * The developed algorithm provides a new paradigm for identifying essential system components.
• * This work bridges the gap between ML interpretability and physical theory development.
• * Paves the way for automated theory building through interpretable ML.