[Arxiv 2024] PrefixQuant: Static Quantization Beats Dynamic through Prefixed Outliers in LLMs

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Contents

• Introduction
• Method
• Experiments
• References

Introduction

• 作者提出 PrefixQuant，基于 QuaRot，通过在 WA 量化时保持关键词元无损并加上 EfficientQAT 微调，能在 W4A4 static quantization 上做到比较好的量化效果；但和 CusionCache 一样，PrefixQuant 尽管可以保持所有关键词元无损，但却没有讨论过加上 prefix 后会对模型精度产生怎样的影响

Method

• 作者发现，对于 static quantization，由于关键词元与其他词元的激活值分布显著不同，如果不对关键词元做特殊处理，校准得到的量化参数会损害非关键词元的量化精度，例如关键词元的 down_proj 输入上会存在 massive outlier、KV cache 则会特别平坦；如果能保持关键词元无损，对其他 tokens 做校准，就能得到更小的量化范围，提升量化精度
• Definition of Outlier Token. 通过 down proj 的输入激活值定位关键词元
  其中， η = 64 \eta=64 η=64
  
• Number of Outlier Tokens. 通过校准集统计出每种模型中关键词元的数量 o = ⌈ max ⁡ ( O ) ⌉ o=\lceil\max(\mathbf O)\rceil o=⌈max(O)⌉，其中 O ∈ R b \mathbf O\in\R^b O∈Rb 为所有 transformer block 中统计的关键词元数量
• Which Tokens to Prefix? top- o o o high-frequency outlier tokens + [BOS]
  

---

• Block-wise Fine-tuning. 采用 EfficientQAT 微调 scale & weights

Experiments

• Settings. 权重 per-channel symmetric quantization，KV cache per-head symmetric static quantization for 4-bit and per-tensor symmetric static quantization for 8-bit，激活值 per-tensor static quantization；校准数据集为 8 Pile samples with a 1024 sequence length，通过 grid search 找到 scale 初始值；微调数据集为 512 samples from Pile with a 1024 context length

---

• Comparison Results.
  
• Results on weight-only quantization.
  
• Inference Speed. (1) Static Quantization Speedup.
  (2) Linear Layer Speedup. For low-bit matrix multiplication, we use the 4-bit GEMM kernel from CUTLASS and design a custom kernel for W4A4 GEMV. We also integrate the de-quantization process into the GEMM and GEMV kernels.
  (3) End-to-end speedup. 这里测速没有用 KV cache 量化 (it saves memory footprint through more computation overhead and only achieves speedup with large batch sizes)
  
• Ablation Studies. (1) Main Components.
  (2) Number of Prefixed Tokens.(3) Content of Prefixed Tokens.
  
• Quantization Time.
  

References

• Chen, Mengzhao, et al. “PrefixQuant: Static Quantization Beats Dynamic through Prefixed Outliers in LLMs.” arXiv preprint arXiv:2410.05265 (2024).
• code: https://github/chenmnz/prefixquant

Contents

• Introduction
• Method
• Experiments
• References

Introduction

• 作者提出 PrefixQuant，基于 QuaRot，通过在 WA 量化时保持关键词元无损并加上 EfficientQAT 微调，能在 W4A4 static quantization 上做到比较好的量化效果；但和 CusionCache 一样，PrefixQuant 尽管可以保持所有关键词元无损，但却没有讨论过加上 prefix 后会对模型精度产生怎样的影响

Method

• 作者发现，对于 static quantization，由于关键词元与其他词元的激活值分布显著不同，如果不对关键词元做特殊处理，校准得到的量化参数会损害非关键词元的量化精度，例如关键词元的 down_proj 输入上会存在 massive outlier、KV cache 则会特别平坦；如果能保持关键词元无损，对其他 tokens 做校准，就能得到更小的量化范围，提升量化精度
• Definition of Outlier Token. 通过 down proj 的输入激活值定位关键词元
  其中， η = 64 \eta=64 η=64
  
• Number of Outlier Tokens. 通过校准集统计出每种模型中关键词元的数量 o = ⌈ max ⁡ ( O ) ⌉ o=\lceil\max(\mathbf O)\rceil o=⌈max(O)⌉，其中 O ∈ R b \mathbf O\in\R^b O∈Rb 为所有 transformer block 中统计的关键词元数量
• Which Tokens to Prefix? top- o o o high-frequency outlier tokens + [BOS]
  

---

• Block-wise Fine-tuning. 采用 EfficientQAT 微调 scale & weights

Experiments

• Settings. 权重 per-channel symmetric quantization，KV cache per-head symmetric static quantization for 4-bit and per-tensor symmetric static quantization for 8-bit，激活值 per-tensor static quantization；校准数据集为 8 Pile samples with a 1024 sequence length，通过 grid search 找到 scale 初始值；微调数据集为 512 samples from Pile with a 1024 context length

---

• Comparison Results.
  
• Results on weight-only quantization.
  
• Inference Speed. (1) Static Quantization Speedup.
  (2) Linear Layer Speedup. For low-bit matrix multiplication, we use the 4-bit GEMM kernel from CUTLASS and design a custom kernel for W4A4 GEMV. We also integrate the de-quantization process into the GEMM and GEMV kernels.
  (3) End-to-end speedup. 这里测速没有用 KV cache 量化 (it saves memory footprint through more computation overhead and only achieves speedup with large batch sizes)
  
• Ablation Studies. (1) Main Components.
  (2) Number of Prefixed Tokens.(3) Content of Prefixed Tokens.
  
• Quantization Time.
  

References

• Chen, Mengzhao, et al. “PrefixQuant: Static Quantization Beats Dynamic through Prefixed Outliers in LLMs.” arXiv preprint arXiv:2410.05265 (2024).
• code: https://github/chenmnz/prefixquant

本文标签： staticQuantizationPrefixQuantarxivOutliers