The Impact of Symmetry on Data Efficiency

This is a study that measured, through actual scaling laws, the theoretical prediction that Equivariance in Geometric Deep Learning reduces sample complexity by a factor of the group size $|G|$.

As a result of the study, the data exchange rate ($eta_{diff}$) was measured at approximately 1.28, showing a tendency to align with the theoretical prediction of 1.0. This demonstrates that equivariant models effectively reduce data requirements compared to general models.

The key findings are as follows:

• Harm from applying incorrect symmetry: When wrong cyclic symmetry is applied to a model, performance is significantly degraded compared to an unconstrained model. This shows that a mismatch in symmetry can go beyond simple invalidation and directly harm model performance.
• Relationship between architecture and augmentation: In output-pooling structures, combining data augmentation with test-time orbit averaging alone can achieve mathematically perfect equivariance.

The study transparently discloses uncertain aspects such as limitations in the estimation method and reproducibility issues, and presents the 'performance degradation when the wrong group is applied' in particular as its most robust result.