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Swift-SVD, a novel activation-aware, closed-form compression framework, is introduced to address the limitations of existing SVD-based LLM compression methods. It achieves theoretical optimality in reconstruction error, practical efficiency, and numerical stability by incrementally aggregating covariance of output activations and performing a single eigenvalue decomposition. Experiments across six LLMs and eight datasets demonstrate that Swift-SVD outperforms state-of-the-art baselines, achieving optimal compression accuracy with significant speedups (3-70X) in end-to-end compression time.
Forget slow, suboptimal SVD compression: Swift-SVD delivers theoretically optimal low-rank LLM compression with 3-70x speedups.
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.
