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Optimizer and Learning Rate Schedule

The training process utilized the Adam optimizer with hyperparameter settings β1=0.9\beta_1 = 0.9, β2=0.98\beta_2 = 0.98, and ϵ=109\epsilon = 10^{-9}.

The learning rate was modulated dynamically across steps according to the following formula:

lrate=dmodel0.5min(step_num0.5,step_numwarmup_steps1.5)lrate = d_{\text{model}}^{-0.5} \cdot \min(step\_num^{-0.5}, step\_num \cdot warmup\_steps^{-1.5})

This schedule increases the learning rate linearly during the initial warmup_stepswarmup\_steps phase. Following the warm-up period, the learning rate decays proportionally to the inverse square root of the step number (step_num0.5step\_num^{-0.5}). In the reported experiments, warmup_steps=4000warmup\_steps = 4000.

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Updated 2026-09-07

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