Logarithmic-time Schedules for Scaling Language Models with Momentum
This addresses the challenge of optimizing training efficiency for large language models, offering a novel method that is incremental but provides substantial practical benefits.
The paper tackles the problem of fixed hyperparameters in AdamW for large-scale language model training by introducing logarithmic-time schedules for (β1, β2, λ), resulting in up to 40% compute efficiency gains compared to tuned AdamW, with improvements that scale with model size.
In practice, the hyperparameters $(β_1, β_2)$ and weight-decay $λ$ in AdamW are typically kept at fixed values. Is there any reason to do otherwise? We show that for large-scale language model training, the answer is yes: by exploiting the power-law structure of language data, one can design time-varying schedules for $(β_1, β_2, λ)$ that deliver substantial performance gains. We study logarithmic-time scheduling, in which the optimizer's gradient memory horizon grows with training time. Although naive variants of this are unstable, we show that suitable damping mechanisms restore stability while preserving the benefits of longer memory. Based on this, we present ADANA, an AdamW-like optimizer that couples log-time schedules with explicit damping to balance stability and performance. We empirically evaluate ADANA across transformer scalings (45M to 2.6B parameters), comparing against AdamW, Muon, and AdEMAMix. When properly tuned, ADANA achieves up to 40% compute efficiency relative to a tuned AdamW, with gains that persist--and even improve--as model scale increases. We further show that similar benefits arise when applying logarithmic-time scheduling to AdEMAMix, and that logarithmic-time weight-decay alone can yield significant improvements. Finally, we present variants of ADANA that mitigate potential failure modes and improve robustness.