Approximation-Generalization Trade-offs under (Approximate) Group Equivariance

Understand

The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models.

• For example, group equivariant neural networks have demonstrated impressive performance across various domains and applications such as protein and drug design.
• A prevalent intuition about such models is that the integration of relevant symmetry results in enhanced generalization.
• Moreover, it is posited that when the data and/or the model may only exhibit $\textit{approximate}$ or $\textit{partial}$ symmetry, the optimal or best-performing model is one where the model symmetry aligns with the data symmetry.