Flat Loss, Evolving Features: Grokking in Modular Addition
Can a network keep learning while its training cross-entropy stays nearly flat at a positive level? We show that it can. On modular addition, a standard testbed for grokking, ReLU networks trained with supported-Polar hidden updates, normalized output-layer updates and weight decay can keep 100% training accuracy while their hidden features change and held-out accuracy rises from zero to above 90%, at relatively flat training cross-entropy. Correct classification need not minimize cross-entropy, which still depends on prediction confidence. We prove this coexistence for one-hidden-layer networks in two finite-window theorems from constructed initializations: one gives a constant gain in t...
| Authors | Akash Kumar, Karthik Sankaranarayanan |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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