Hyperball May Not Be a Free Lunch
For scale-invariant deep networks, Hyperball-style optimizers have shown strong performance in large-scale training by fixing the norms of matrix-valued parameters and normalizing updates. However, the source of their advantage remains unclear. Starting from the angular displacement between consecutive parameter states, we derive an angular effective learning rate that accounts for the parameter-update angle, parameter norm, and update norm. We also show that the conventional norm-based measure is a special case under parameter-update orthogonality. We then decompose optimizer updates into radial and tangential components and analyze how radial updates affect one-step angular displacement...
| Authors | Yihao Xiao, Jialong Sun, Zitian Gao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 24 July 2026 |
| Last updated at source | 24 July 2026 |
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