@article{revealingmodulargradientnoiseimbalancein,
  title = {Revealing Modular Gradient Noise Imbalance in LLMs: Calibrating Adam via Signal-to-Noise Ratio},
  author = {Ziqing Wen and Zhouyang Liu and Jiahuan Wang and Ping Luo and Li Shen and Dongsheng Li and Tao Sun},
  year = {2026},
  eprint = {2605.05794},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.05794},
}