ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals

Utkarsh Saxena, Sayeh Sharify, Kaushik Roy, Xin Wang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:53095-53114, 2025.

Abstract

Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3X speedup over 16-bit baseline. Anonymous code repository available at https://anonymous.4open.science/r/project-resq-2142.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-saxena25b, title = {{R}es{Q}: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals}, author = {Saxena, Utkarsh and Sharify, Sayeh and Roy, Kaushik and Wang, Xin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {53095--53114}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/saxena25b/saxena25b.pdf}, url = {https://proceedings.mlr.press/v267/saxena25b.html}, abstract = {Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3X speedup over 16-bit baseline. Anonymous code repository available at https://anonymous.4open.science/r/project-resq-2142.} }
Endnote
%0 Conference Paper %T ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals %A Utkarsh Saxena %A Sayeh Sharify %A Kaushik Roy %A Xin Wang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-saxena25b %I PMLR %P 53095--53114 %U https://proceedings.mlr.press/v267/saxena25b.html %V 267 %X Post-training quantization (PTQ) of large language models (LLMs) holds the promise in reducing the prohibitive computational cost at inference time. Quantization of all weight, activation and key-value (KV) cache tensors to 4-bit without significantly degrading generalizability is challenging, due to the high quantization error caused by extreme outliers in activations. To tackle this problem, we propose ResQ, a PTQ method that pushes further the state-of-the-art. By means of principal component analysis (PCA), it identifies a low-rank subspace (in practice 1/8 of the hidden dimension) in which activation variances are highest, and keep the coefficients within this subspace in high precision, e.g. 8-bit, while quantizing the rest to 4-bit. Within each subspace, invariant random rotation is applied to further suppress outliers. We show that this is a provably optimal mixed precision quantization scheme that minimizes error. With the Llama and Qwen2.5 families of models, we demonstrate that ResQ outperforms recent uniform and mixed precision PTQ methods on a variety of benchmarks, achieving up to 33% lower perplexity on Wikitext than the next best method SpinQuant, and upto 3X speedup over 16-bit baseline. Anonymous code repository available at https://anonymous.4open.science/r/project-resq-2142.
APA
Saxena, U., Sharify, S., Roy, K. & Wang, X.. (2025). ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:53095-53114 Available from https://proceedings.mlr.press/v267/saxena25b.html.

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