Zero Sum SVD: Balancing Loss Sensitivity for Low Rank LLM Compression

arXiv:2602.02848v2 Announce Type: replace Abstract: Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet performance depends on how rank is allocated under a global compression ratio. Prior methods often use homogeneous ranks for similarly sized matrices, despite large differences in loss sensitivity, or rely on expensive iterative pre-truncation optimization to determine per matrix ranks. We propose Zero Sum SVD (ZS-SVD), a post-training method that performs global singular component selection using activation whitening and first-order calibration loss estimates in whitened coordinates. ZS-SVD prunes components across the whole model with a zero sum rule that keeps the cumulative predicted loss change near zero, automatically yielding heterogeneous ranks without solving a rank allocation optimization. Motivated by evidence that gradients near pretrained solutions exhibit low rank structure, we also introduce an optional lightweight correction that applies a single projected gradient update after truncation, followed by re-truncation. Extensive experiments across multiple LLM architectures show consistent gains across diverse benchmarks and compression ratios. Code is available at https://github.com/mint-vu/Zero-Sum-SVD

Abstract:Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet performance depends on how rank is allocated under a global compression ratio. Prior methods often use homogeneous ranks for similarly sized matrices, despite large differences in loss sensitivity, or rely on expensive iterative pre-truncation optimization to determine per matrix ranks. We propose Zero Sum SVD (ZS-SVD), a post-training method that performs global singular component selection using activation whitening and first-order calibration loss estimates in whitened coordinates. ZS-SVD prunes components across the whole model with a zero sum rule that keeps the cumulative predicted loss change near zero, automatically yielding heterogeneous ranks without solving a rank allocation optimization. Motivated by evidence that gradients near pretrained solutions exhibit low rank structure, we also introduce an optional lightweight correction that applies a single projected gradient update after truncation, followed by re-truncation. Extensive experiments across multiple LLM architectures show consistent gains across diverse benchmarks and compression ratios. Code is available at this https URL

Machine Learning (cs.LG)

arXiv:2602.02848 [cs.LG]

(or arXiv:2602.02848v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2602.02848 Focus to learn more arXiv-issued DOI via DataCite

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Zero Sum SVD: Balancing Loss Sensitivity for Low Rank LLM Compression

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