Ori: Drift-Aware Streaming $k$-PCA for Very Low-Rank LLM Training
A prominent family of low-rank LLM optimizers, pioneered by GaLore, performs gradient-subspace projection: at each step, they project the gradient into a low-dimensional subspace and map the update back to the full model. Most existing work either recomputes the gradient subspace at certain intervals, or performs post-hoc adaptation to catch up to the moving subspace. In this work, we explicitly identify in practice the slow, stable manner in which LLM gradient subspaces drift across time. To this end, we propose Ori, a novel low-rank optimizer for training LLMs that captures the shifting principal gradient directions over time to achieve state-of-the-art accuracy under stringent low-rank...
| Authors | Xinyu Luo, Jincheng Zhou, Mengbo Wang et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 October 2026 |
| Last updated at source | 16 October 2026 |
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