Low-Rank Friction for Memory-Efficient Transformer Pretraining

תקציר מקורי באנגליתarXiv:2609.30342v2 Announce Type: cross Abstract: 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 $\xi\in\mathbb{R}^{m\times n}$ carries the same $\mathcal{O}(mn)$ memory overhead per layer as Adam's second-moment buffer. Here we replace iKFAD's friction tensor $\xi$ 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 parity in performance with iKFAD: experiments on GP