Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909038800797696 |
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| author | Cho, Yoonjun Jeon, Dongjae Kim, Soeun Jeon, Moongyu No, Albert |
| author_facet | Cho, Yoonjun Jeon, Dongjae Kim, Soeun Jeon, Moongyu No, Albert |
| contents | Quantization Error Reconstruction (QER) reduces accuracy loss in Post-Training Quantization (PTQ) by approximating weights as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$, using a rank-$r$ correction to reconstruct quantization error. Prior methods devote the full rank budget to error reconstruction, which is suboptimal when $\mathbf{W}$ has intrinsic low-rank structure and quantization corrupts dominant directions. We propose Structured Residual Reconstruction (SRR), a rank-allocation framework that preserves the top-$k$ singular subspace of the activation-scaled weight before quantization, quantizes only the residual, and uses the remaining rank $r-k$ for error reconstruction. We derive a theory-guided criterion for selecting $k$ by balancing quantization-exposed energy and unrecoverable error under rank constraints. We further show that resulting $\mathbf{Q} + \mathbf{L}\mathbf{R}$ parameterization naturally supports Quantized Parameter-Efficient Fine-Tuning (QPEFT), and stabilizes fine-tuning via gradient scaling along preserved directions. Experiments demonstrate consistent perplexity reductions across diverse models and quantization settings in PTQ, along with a 5.9 percentage-point average gain on GLUE under 2-bit QPEFT. The project page is available at https://ai-isl.github.io/srr. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_02001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs Cho, Yoonjun Jeon, Dongjae Kim, Soeun Jeon, Moongyu No, Albert Machine Learning Artificial Intelligence Quantization Error Reconstruction (QER) reduces accuracy loss in Post-Training Quantization (PTQ) by approximating weights as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$, using a rank-$r$ correction to reconstruct quantization error. Prior methods devote the full rank budget to error reconstruction, which is suboptimal when $\mathbf{W}$ has intrinsic low-rank structure and quantization corrupts dominant directions. We propose Structured Residual Reconstruction (SRR), a rank-allocation framework that preserves the top-$k$ singular subspace of the activation-scaled weight before quantization, quantizes only the residual, and uses the remaining rank $r-k$ for error reconstruction. We derive a theory-guided criterion for selecting $k$ by balancing quantization-exposed energy and unrecoverable error under rank constraints. We further show that resulting $\mathbf{Q} + \mathbf{L}\mathbf{R}$ parameterization naturally supports Quantized Parameter-Efficient Fine-Tuning (QPEFT), and stabilizes fine-tuning via gradient scaling along preserved directions. Experiments demonstrate consistent perplexity reductions across diverse models and quantization settings in PTQ, along with a 5.9 percentage-point average gain on GLUE under 2-bit QPEFT. The project page is available at https://ai-isl.github.io/srr. |
| title | Preserve-Then-Quantize: Balancing Rank Budgets for Quantization Error Reconstruction in LLMs |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.02001 |