FlatQuant: Flatness Matters for LLM Quantization

Yuxuan Sun, Ruikang Liu, Haoli Bai, Han Bao, Kang Zhao, Yuening Li, Jiaxin Hu, Xianzhi Yu, Lu Hou, Chun Yuan, Xin Jiang, Wulong Liu, Jun Yao
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57587-57613, 2025.

Abstract

Recently, quantization has been widely used for the compression and acceleration of large language models (LLMs). Due to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with equally spaced quantization points. Prior research explores various pre-quantization transformations to suppress outliers, such as per-channel scaling and Hadamard transformation. However, we observe that these transformed weights and activations can still exhibit steep and dispersed distributions. In this paper, we propose FlatQuant (Fast and Learnable Affine Transformation), a new post-training quantization approach that enhances the flatness of weights and activations. Our approach identifies optimal affine transformations for each linear layer, calibrated in hours via a lightweight objective. To reduce runtime overhead of affine transformation, we apply Kronecker product with two lightweight matrices, and fuse all operations in FlatQuant into a single kernel. Extensive experiments demonstrate that FlatQuant establishes a new state-of-the-art benchmark for quantization. For example, it achieves less than 1% accuracy drop for W4A4 quantization on the LLaMA-3-70B model, surpassing SpinQuant by 7.5%. Additionally, it provides up to 2.3x prefill speedup and 1.7x decoding speedup compared to the FP16 model. Code is available at: https://github.com/ruikangliu/FlatQuant.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-sun25l, title = {{F}lat{Q}uant: Flatness Matters for {LLM} Quantization}, author = {Sun, Yuxuan and Liu, Ruikang and Bai, Haoli and Bao, Han and Zhao, Kang and Li, Yuening and Hu, Jiaxin and Yu, Xianzhi and Hou, Lu and Yuan, Chun and Jiang, Xin and Liu, Wulong and Yao, Jun}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57587--57613}, 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/sun25l/sun25l.pdf}, url = {https://proceedings.mlr.press/v267/sun25l.html}, abstract = {Recently, quantization has been widely used for the compression and acceleration of large language models (LLMs). Due to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with equally spaced quantization points. Prior research explores various pre-quantization transformations to suppress outliers, such as per-channel scaling and Hadamard transformation. However, we observe that these transformed weights and activations can still exhibit steep and dispersed distributions. In this paper, we propose FlatQuant (Fast and Learnable Affine Transformation), a new post-training quantization approach that enhances the flatness of weights and activations. Our approach identifies optimal affine transformations for each linear layer, calibrated in hours via a lightweight objective. To reduce runtime overhead of affine transformation, we apply Kronecker product with two lightweight matrices, and fuse all operations in FlatQuant into a single kernel. Extensive experiments demonstrate that FlatQuant establishes a new state-of-the-art benchmark for quantization. For example, it achieves less than 1% accuracy drop for W4A4 quantization on the LLaMA-3-70B model, surpassing SpinQuant by 7.5%. Additionally, it provides up to 2.3x prefill speedup and 1.7x decoding speedup compared to the FP16 model. Code is available at: https://github.com/ruikangliu/FlatQuant.} }
Endnote
%0 Conference Paper %T FlatQuant: Flatness Matters for LLM Quantization %A Yuxuan Sun %A Ruikang Liu %A Haoli Bai %A Han Bao %A Kang Zhao %A Yuening Li %A Jiaxin Hu %A Xianzhi Yu %A Lu Hou %A Chun Yuan %A Xin Jiang %A Wulong Liu %A Jun Yao %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-sun25l %I PMLR %P 57587--57613 %U https://proceedings.mlr.press/v267/sun25l.html %V 267 %X Recently, quantization has been widely used for the compression and acceleration of large language models (LLMs). Due to the outliers in LLMs, it is crucial to flatten weights and activations to minimize quantization error with equally spaced quantization points. Prior research explores various pre-quantization transformations to suppress outliers, such as per-channel scaling and Hadamard transformation. However, we observe that these transformed weights and activations can still exhibit steep and dispersed distributions. In this paper, we propose FlatQuant (Fast and Learnable Affine Transformation), a new post-training quantization approach that enhances the flatness of weights and activations. Our approach identifies optimal affine transformations for each linear layer, calibrated in hours via a lightweight objective. To reduce runtime overhead of affine transformation, we apply Kronecker product with two lightweight matrices, and fuse all operations in FlatQuant into a single kernel. Extensive experiments demonstrate that FlatQuant establishes a new state-of-the-art benchmark for quantization. For example, it achieves less than 1% accuracy drop for W4A4 quantization on the LLaMA-3-70B model, surpassing SpinQuant by 7.5%. Additionally, it provides up to 2.3x prefill speedup and 1.7x decoding speedup compared to the FP16 model. Code is available at: https://github.com/ruikangliu/FlatQuant.
APA
Sun, Y., Liu, R., Bai, H., Bao, H., Zhao, K., Li, Y., Hu, J., Yu, X., Hou, L., Yuan, C., Jiang, X., Liu, W. & Yao, J.. (2025). FlatQuant: Flatness Matters for LLM Quantization. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57587-57613 Available from https://proceedings.mlr.press/v267/sun25l.html.

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