Muon在大模型上加速效果缩水？Hyperball通过固定矩阵范数，让Muon在1.2B Qwen3上又快了20-30%，还更好调参。
论文提出Hyperball，一种简单优化器包装器，固定权重矩阵及其更新量的Frobenius范数，解决Muon等优化器在大模型（如1.2B参数Qwen3模型）上相比AdamW加速效果衰减的问题。实验表明，Muon+Hyperball实现20-30% token等效加速，并改善学习率在宽度和深度上的迁移。该方法受理论启发：权重衰减导致平衡权重范数仅依赖于超参数，进而决定角度学习率。
Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimization
Matrix based optimizers such as Muon can substantially speed up language model pretraining, but their gains over AdamW are observed to shrink as model size and data scale grow when using standard constant decoupled weight decay. We propose Hyperball, a simple optimizer wrapper that addresses this issue. Given a base optimizer such as Adam or Muon, Hyperball sets the Frobenius norms of weight matrices and their corresponding optimizer updates to fixed constants. On Qwen3 style models up to 1.2B parameters, Muon Hyperball achieves 20--30% token equivalent speedup over weight decay baselines. Hyperball also improves learning rate transfer across widths and depths compared to decoupled weight decay. This method is motivated by prior theory showing that training with weight decay leads to an equilibrium weight norm that only depends on the training hyperparameters. Through this mechanism, the weight decay then decides the angular learning rate, i.e. how fast the direction of the weight matrix changes.