Learning a local symmetry with neural networks.

Area of Science:

• Theoretical Physics
• Machine Learning
• Computational Science

Background:

• Gauge symmetry Z_{2} is fundamental in diverse physical systems, including topological transitions and quantum chromodynamics.
• This symmetry significantly influences the computational difficulty of spin-glass problems.
• Understanding and detecting gauge symmetry is vital for advancing theoretical and computational physics.

Purpose of the Study:

• To investigate the capability of neural networks in identifying the complex gauge symmetry Z_{2}.
• To develop a method for learning gauge symmetry and generating compressed latent representations of gauge orbits.
• To address the computational challenges associated with system-wrapping loops, such as Polyakov loops.

Main Methods:

• Designing a specialized neural network architecture.
• Creating a tailored dataset for training the neural network.
• Implementing techniques to specifically handle system-wrapping loops (Polyakov loops).

Main Results:

• Demonstrated the neural network's capacity to successfully learn and detect Z_{2} gauge symmetry.
• Achieved compressed latent representations of gauge orbits, simplifying complex data.
• Showcased the method's effectiveness in addressing computationally relevant features like Polyakov loops.

Conclusions:

• Neural networks offer a powerful tool for detecting complex symmetries in physical systems.
• The developed method provides a novel approach to analyze and simplify problems governed by gauge symmetry.
• This work has implications for computational complexity and the study of systems with topological properties.