Spectral Initialization and Certification for Power System Angle Estimation

What the math gives to ML

The paper identifies a useful pattern for nonconvex problems with a global phase gauge: spectral initialization succeeds when perturbation size is small relative to a constrained observability margin, and the remaining ambiguity is removed by fixing the gauge. This structure transfers naturally to neural modules that estimate per-node or per-view rotations from noisy pairwise relative measurements, such as graph representation alignment, multi-view embedding alignment, and phase-valued latent variables. Rather than initializing these variables randomly and relying on nonlinear optimization, construct a connection matrix, extract its leading eigenvector, normalize each component onto the unit circle, and use the Jacobian spectral gap to decide whether the initialization is trustworthy. The strongest first experiment is a graph-alignment front end whose synchronized rotations initialize a downstream GNN or contrastive embedding model.