Deciphering Two Training Clocks in Grokking via Deep Linear Network Theory with Conditional ReLU Reduction
Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales. We formalize this phenomenon by separating the fast decay of the classification loss from the slower simplification of the learned representation, and we call the resulting pair of stopping times two training clocks. For deep linear networks, we show that a post-margin gap-growth or one-step tail-contraction condition reduces the cross-entropy loss to level epsilon on a logarithmic time scale. In contrast, when layerwise weight decay is present, the induced regularization on the end-to-end map can be expressed as a Schatten-type penalty; under a sharp late-time Kurdyk...
| Authors | Hu Tan, Kuo Gai, Shihua Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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