Frustration without Glass: A Non-Abelian Gauge Model of Network Compatibility
arXiv:2608.17817
2026
Architecture
1 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper offers a non-Abelian gauge mechanism for separating local consistency from global compatibility: edge transformations may be locally valid while plaquette holonomies remain frustrated around loops. Its transferable asset is a gauge-invariant loop-consistency functional, together with compatibility and susceptibility diagnostics that distinguish coherent structure from independent noise and correlated frustration. A neural implementation can assign SU(2) transport operators to graph edges, use Wilson-loop penalties during training, and monitor the predicted disorder-driven compatibility transition.
Ideas from this paper
✗ Failed on benchmark
2026
Attach an SU(2) transport matrix to every directed edge of a graph neural network and penalize nontrivial plaquette holonomies instead of penalizing individual edge transformations. The regularizer is invariant to arbitrary local changes of latent representation frame, encouraging path-consistent relational features without requiring all edges to share one global coordinate system.
Useful7/10
Difficulty6/10
Novelty7/10