Distributional Spectral Diagnostics for Localizing Grokking Transitions
In grokking, a model first fits the training data while test accuracy remains low, and only later begins to generalize. We ask whether this transition can be localized from observed training trajectories before the test accuracy rises, and formulate grokking transition localization as a diagnostic problem with an explicit threshold/FPR/lead-time trade-off. Task-dependent observables are summarized as empirical distributions, mapped to Wasserstein/quantile coordinates, and analyzed by Hankel dynamic mode decomposition (DMD); the resulting reconstruction residual, together with spectrum and effective rank, forms the diagnostic output. On held-out modular-addition Transformer runs, the resid...
| Authors | Ziyue Wang, Yufeng Ying, Takafumi Kanamori |
|---|---|
| Primary category | cs.LG |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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