A Refresh Interval Does Not Fully Specify a Refresh Schedule: Learning-Rate-Dependent Placement in Kronecker-Preconditioned Language Model Training
Kronecker-preconditioned optimizers recompute a cached curvature eigendecomposition only periodically, and implementations and adaptive methods control this through the refresh frequency. We show that frequency leaves part of a schedule free: at a fixed number of refreshes, when they occur changes held-out loss at the same compute. Training GPT-style models with the Mousse optimizer across model sizes, we move the middle refreshes of a four-refresh schedule while fixing the first and last. On FineWeb the two placements exchanged rank as the learning rate rose (later placement was better at low rates, earlier placement at high ones), so a single-learning-rate comparison can report either r...
| Authors | Xinyu Wang, Zhiwei Zhai, Yu Gu et al. |
|---|---|
| Primary category | cs.LG |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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