Rounding in Preconditioner Space: Redesigning 4-bit AdamW Optimizer-State Quantization
Quantizing AdamW's optimizer states reduces persistent storage, but quantization errors propagate through the moment recurrences and perturb subsequent adaptive updates. We redesign 4-bit optimizer-state quantization for AdamW from the perspective of \emph{rounding space}: the coordinate in which a quantizer chooses between adjacent reconstruction levels. For the second moment, a local analysis of the quantization cell adjacent to zero shows that small mean state error need not imply small mean preconditioner error at the next step. A one-dimensional quadratic construction further shows qualitatively different optimization dynamics under state-space and preconditioner-space rounding. Thes...
| Authors | Hanyang Li, Shao Tang, Daniel Thomas Braithwaite et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 October 2026 |
| Last updated at source | 8 October 2026 |
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