Universality Classes of Spectral Learning Dynamics

Modern learning systems appear algorithmically diverse yet empirically convergent toward a small set of training regimes. We propose a universality framework in which optimization dynamics are classified by spectral invariants rather than by optimizer-specific update rules. We define a common spectral state process, identify invariant scaling signatures, and show that SGD-, Adam-, and attention-driven training trajectories fall into a finite set of universality classes under mild regularity assumptions.