Group-Resolved Weight Decay Controls Grokking Arrival Across Checkpoint States

Does grokking depend only on how much weight decay is applied, or also on where it is applied? We study two-layer Transformers using paired continuations from complete checkpoint states. We allocate decay between internal computation parameters (attention, MLP, LayerNorm; GC) and input/output parameters (embedding, head; EH), matching initial decay-only squared-norm contraction. On modular addition, shifting this matched total from EH toward GC advances sustained high test accuracy by $2,100$ steps on average, with the same direction in all 12 parents. Both groups accelerate arrival, but GC has the larger response in the tested dose units. At early checkpoints, high-GC continuations arrive in $63/64$ cases within $8,000$ steps, versus $0/64$ under low GC. Extending all 128 low- and intermediate-GC arms to $32,000$ steps yields arrival in every arm: the short-budget gap reflects delay for these runs, not permanent failure. The fixed allocation swap also advances arrival on $S_5$ permutation composition. Separate parameter-source interventions and a one-step response assay characterize complementary effects of inherited state, without establishing a mechanism for arrival. These results identify decay allocation as a control of grokking timing and show why finite-budget completion must be distinguished from eventual generalization.