Symmetry discovery for different data types.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Computational Science

Background:

• Equivariant neural networks leverage data symmetries for enhanced generalization.
• Current methods require predefined knowledge of data types and symmetries, limiting applicability.
• Discovering these symmetries automatically is a significant challenge in machine learning.

Purpose of the Study:

• To propose LieSD, a novel method for discovering continuous group symmetries from data using trained neural networks.
• To characterize equivariance and invariance through Lie algebra, enabling direct computation from network inputs, outputs, and gradients.
• To extend LieSD for handling multi-channel and tensor data.

Main Methods:

• LieSD approximates task input-output mappings with neural networks.
• It utilizes Lie algebra to represent continuous group symmetries.
• The method directly solves the Lie algebra space using network gradients and data.

Main Results:

• LieSD accurately determines the number of Lie algebra bases without costly group sampling.
• The method demonstrates robust performance on non-uniform datasets, outperforming Generative Adversarial Network (GAN)-based approaches.
• Validation was successful on diverse tasks including physics simulations, particle physics, and image recognition (rotated MNIST).

Conclusions:

• LieSD offers an effective, data-driven approach to discovering symmetries for equivariant neural networks.
• It overcomes limitations of methods requiring prior symmetry knowledge and performs well on challenging datasets.
• The method advances the development of more generalizable and robust AI models.