GradPower: Powering Gradients for Faster Language Model Pre-Training

We propose **GradPower**, a lightweight gradient-transformation technique for accelerating language model pre-training. Given a gradient vector $\boldsymbol{g}=(g\_{i})\_{i}$, GradPower first applies the elementwise `sign-power` transformation: $ \varphi_p(\boldsymbol{g}) = \left({\rm sign}(g\_i)|g\_i|^p\right)\_{i} $ for a fixed $p>0$, and then feeds the transformed gradient into a base optimizer. Notably, GradPower requires only a **single-line code change** and no modifications to the base optimizer’s internal logic, including the hyperparameters. When applied to AdamW (termed **AdamWPower**), GradPower consistently achieves lower terminal loss across diverse architectures (LLaMA, Qwen2MoE), parameter scales (66M to 2B), datasets (C4, OpenWebText), and learning-rate schedules (cosine, warmup-stable-decay). The most pronounced gains are observed when training modern mixture-of-experts models with warmup-stable-decay schedules. GradPower also integrates seamlessly with other state-of-the-art optimizers, such as Muon, yielding further improvements. Finally, we provide theoretical analyses that reveal the underlying mechanism of GradPower and highlight the influence of gradient noise.