Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networks
Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, show...
| Authors | Ali Rayat, Gia-Wei Chern |
|---|---|
| Primary category | cond-mat.stat-mech |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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