Researchers discover that spectral entropy collapse reliably predicts when AI models suddenly generalize after memorization, enabling 1,000+ step advance warning of the grokking transition.

Grokking follows a two-phase pattern: norm expansion followed by entropy collapse, with normalized spectral entropy serving as a measurable order parameter for the transition

The entropy metric crosses a stable threshold of ~0.61 before generalization in 100% of test runs, providing an average 1,020-step lead time for prediction

Causal experiments confirm entropy (not norm magnitude) drives grokking: blocking entropy collapse delays generalization by 5,020 steps while norm-matched controls show no effect

A power-law model predicts grokking onset with 4.1% error across different group-theoretic tasks, including both abelian and non-abelian groups