From $O(mn)$ to $O(r^2)$: Two-Sided Low-Rank Communication for Adam in Distributed Training with Memory Efficiency

• URL: http://arxiv.org/abs/2602.08007v1
• Date: Sun, 08 Feb 2026 15:23:09 GMT
• Title: From $O(mn)$ to $O(r^2)$: Two-Sided Low-Rank Communication for Adam in Distributed Training with Memory Efficiency
• Authors: Sizhe Dang, Jiaqi Shao, Xiaodong Zheng, Guang Dai, Yan Song, Haishan Ye,
• Abstract summary: We propose TSR, which brings two-sided low-rank communication to Adam-family updates (TSR-Adam)<n>To further reduce the peak communication from subspace refresh, TSR-Adam adopts a randomized SVD-based refresh that avoids full-gradient synchronization.<n>Across pretraining from 60M to 1B model scales, TSR-Adam reduces average communicated bytes per step by $13times$, and on GLUE fine-tuning it reduces communication by $25times$, while achieving comparable performance.
• Score: 28.885724420612323
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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