Reproduce “Approximately Equivariant Graph Networks” on OpenResearch

About this paper

Ningyuan Huang, Ron Levie, Soledad Villar

The paper differentiates active and passive symmetries in Graph Neural Networks (GNNs) operating on fixed domains, proposing a framework for "approximately equivariant" GNNs through graph coarsening. It theoretically characterizes a bias-variance tradeoff for symmetry choices, demonstrating that optimal generalization often stems from approximate symmetries that balance model expressivity and regularization.

Key insights

• GNN design for fixed graphs should prioritize active symmetries, defined by graph automorphisms or their approximations, over universal permutation equivariance.
• Approximate symmetries, derived from coarsening irregular graphs into more symmetric structures, provide a practical and theoretically grounded approach to leverage symmetry in real-world graphs.
• A quantifiable bias-variance tradeoff exists for symmetry choices in GNNs, where an intermediate level of approximate symmetry often yields the best generalization by balancing expressivity and regularization.

Summary by alphaXiv.