# GradPower: Powering Gradients for Faster Language Model Pre-Training

arXiv: https://arxiv.org/abs/2505.24275 · HTML: https://mlsanity.com/paper/2505.24275/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 57 of its 74 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 57)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [8-bit Optimizers via Block-wise Quantization](https://mlsanity.com/paper/2110.02861/) (2021)
- [An Empirical Model of Large-Batch Training](https://mlsanity.com/paper/1812.06162/) (2018)
- [Sophia: A Scalable Stochastic Second-order Optimizer for Language Model Pre-training](https://mlsanity.com/paper/2305.14342/) (2023)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Small-scale proxies for large-scale Transformer training instabilities](https://mlsanity.com/paper/2309.14322/) (2023)
- [Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing Deep Models](https://mlsanity.com/paper/2208.06677/) (2022)
- [A Simple Convergence Proof of Adam and Adagrad](https://mlsanity.com/paper/2003.02395/) (2020)
- [Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations](https://mlsanity.com/paper/2405.18392/) (2024)

## Built on by (most cited first, 8 of 8)

- [On the Width Scaling of Neural Optimizers Under Matrix Operator Norms I: Row/Column Normalization and Hyperparameter Transfer](https://mlsanity.com/paper/2603.09952/) (2026)
- [Fast Catch-Up, Late Switching: Optimal Batch Size Scheduling via Functional Scaling Laws](https://mlsanity.com/paper/2602.14208/) (2026)
- [Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models](https://mlsanity.com/paper/2605.26895/) (2026)
- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)
- [Effective Learning Rate Governs Loss Dynamics in Language Model Pretraining](https://mlsanity.com/paper/2608.24814/) (2026)
- [Revealing Modular Gradient Noise Imbalance in LLMs: Calibrating Adam via Signal-to-Noise Ratio](https://mlsanity.com/paper/2605.05794/) (2026)
- [Curvature-Conditioned Multiscale Momentum with Sphere Constraints for LLM Pretraining](https://mlsanity.com/paper/2608.28442/) (2026)
- [CAST: History-Adaptive Spectral Clipping for LLM Pretraining](https://mlsanity.com/paper/2610.19761/) (2026)

## Abstract (arXiv)

We propose GradPower, a lightweight gradient-transformation technique for accelerating language model pre-training. Given a gradient vector g=(gi)i, GradPower first applies the elementwise sign-power transformation: varphip(g)=(rm sign(gi)|gi|p)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 Adam (termed AdamPower), 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.