The deployment of Large Language Models is constrained by the memory and bandwidth demands of static weights and dynamic Key-Value cache. SVD-based compression provides a hardware-friendly solution to reduce these costs. However, existing methods suffer from two key limitations: some are suboptimal in reconstruction error, while others are theoretically optimal but practically inefficient. In this paper, we propose Swift-SVD, an activation-aware, closed-form compression framework that simultaneously guarantees theoretical optimum, practical efficiency and numerical stability. Swift-SVD incrementally aggregates covariance of output activations given a batch of inputs and performs a single eigenvalue decomposition after aggregation, enabling training-free, fast, and optimal layer-wise low-rank approximation. We employ effective rank to analyze local layer-wise compressibility and design a dynamic rank allocation strategy that jointly accounts for local reconstruction loss and end-to-end layer importance. Extensive experiments across six LLMs and eight datasets demonstrate that Swift-SVD outperforms state-of-the-art baselines, achieving optimal compression accuracy while delivering 3-70X speedups in end-to-end compression time. Our code will be released upon acceptance.
@article{arxiv.2604.01609,
title = {Swift-SVD: Theoretical Optimality Meets Practical Efficiency in Low-Rank LLM Compression},
author = {Ruoling Qi and Yirui Liu and Xuaner Wu and Xiangyu Wang and Ming Li and Chen Chen and Jian Chen and Yin Chen and Qizhen Weng},
journal= {arXiv preprint arXiv:2604.01609},
year = {2026}
}