As foundation models continue to scale, pretraining increasingly relies on data-parallel distributed optimization, making bandwidth-limited gradient synchronization a key bottleneck. Orthogonally, projection-based low-rank optimizers were mainly designed for memory efficiency, but remain suboptimal for communication-limited training: one-sided synchronization still transmits an $O(rn)$ object for an $m\times n$ matrix gradient and refresh steps can dominate peak communicated bytes. We propose TSR, which brings two-sided low-rank communication to Adam-family updates (TSR-Adam) by synchronizing a compact core $U^\top G V\in\mathbb{R}^{r\times r}$, reducing the dominant per-step payload from $O(mn)$ to $O(r^2)$ while keeping moment states in low-dimensional cores. To further reduce the peak communication from subspace refresh, TSR-Adam adopts a randomized SVD-based refresh that avoids full-gradient synchronization. We additionally extend low-rank communication to embedding gradients with embedding-specific ranks and refresh schedules, yielding additional communication and memory savings over keeping embeddings dense. Across pretraining from 60M to 1B model scales, TSR-Adam reduces average communicated bytes per step by $13\times$, and on GLUE fine-tuning it reduces communication by $25\times$, while achieving comparable performance; we further provide a theoretical stationarity analysis for the proposed update. Code is available at https://github.com/DKmiyan/TSR-Adam.
Conda: Column-Normalized Adam for Training Large Language Models Faster
State Key Lab of General AI, School of Intelligence Science and Technology, Peking University（通用人工智能国家重点实验室，智能科学与技术学院，北京大学）；Singapore Management University（新加坡国立大学）；Nankai University（南开大学）；Beijing Normal University（北京师范大学）；ByteDance Seed（字节跳动种子）；Beijing University of Posts and Telecommunications（北京邮电大学）；Institute for Artificial Intelligence, Peking University（人工智能研究院，北京大学）；Pazhou Laboratory (Huangpu), Guangzhou, Guangdong, China（黄埔实验室（广州），广东，中国）
GWT: Scalable Optimizer State Compression for Large Language Model Training
National Key Laboratory of Parallel and Distributed Computing（并行与分布式计算国家重点实验室）；National University of Defense Technology（国防科技大学）；Center for Machine Learning Research（机器学习研究中心）
TeZO: Empowering the Low-Rankness on the Temporal Dimension in the Zeroth-Order Optimization for Fine-tuning LLMs
Faculty of Engineering, The University of Sydney（悉尼大学工程学院）；School of Cyber Science and Technology, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区网络与空间安全学院）
Institute of Science Tokyo（东京科学研究所）；RIKEN Center for AI Project（理化学研究所AI项目中心）；Technical University of Darmstadt（达姆施塔特工业大学）；Technical University of Munich（慕尼黑工业大学）
A geometric framework for momentum-based optimizers for low-rank training
Computer Science and Mathematics Division（计算机科学与数学 division）；Oak Ridge National Laboratory（橡树岭国家实验室）；Department of Mathematics（数学系）；Otto von Guericke University Magdeburg（奥托·冯·格里克大学马格德堡分校）；Norwegian University of Life Sciences（挪威生命科学大学）
