Low-Rank Friction for Memory-Efficient Transformer Pretraining
iKFAD is a recently proposed optimiser that replaces adaptive learning rates with adaptive friction in the momentum dynamics, yet performs as well as Adam. Its limitation is that the full friction tensor $ξ\in\mathbb{R}^{m\times n}$ carries the same $\mathcal{O}(mn)$ memory overhead per layer as Adam's second-moment buffer. Here we replace iKFAD's friction tensor $ξ$ with a rank-1 outer-product factorisation built from row and column momentum statistics, resulting in Rank-1 iKFAD (R-iKFAD). This reduces the friction memory footprint from $\mathcal{O}(mn)$ to $\mathcal{O}(m+n)$ per layer, which approximately halves iKFAD's total optimiser state. Despite this reduction, R-iKFAD maintains pa...
| Authors | Rajit Rajpal, Benedict Leimkuhler |
|---|---|
| Primary category | stat.ML |
| Published | 24 September 2026 |
| Last updated at source | 28 September 2026 |
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