Grokking Is Conditional and Fragile: A Fully-Tractable, Multi-Seed Study at 12K Parameters
Grokking -- the delayed onset of generalization long after a network has fit its training set - -is usually studied in models too large to read completely and reported from single training runs. We instead study a publicly released ~11,856-parameter Llama-style transformer (Glimmer-1-Base) on modular arithmetic, small enough to enumerate its weights, attention, and full input-output map, and we measure grokking as a multi-seed rate rather than a single outcome. In this fully-tractable regime grokking is a conditional, fragile phase transition. It is gated by training-set coverage, whose threshold tracks output cardinality (the modulus) more than task structure, an ordering that holds abov...
| Authors | Yoshiyuki Ootani |
|---|---|
| Primary category | cs.LG |
| Published | 6 July 2026 |
| Last updated at source | 6 July 2026 |
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