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摘要: Transformer模型具有庞大的参数规模和计算开销, 难以直接部署于资源受限的边缘设备, 限制了其在开放环境中的实际应用.低比特量化能够显著降低模型存储需求并提升推理效率, 是实现Transformer模型轻量化部署的重要技术路径.然而, 现有量化方法通常受固定量化区间约束, 在处理非线性激活产生的长尾分布时, 难以有效平衡裁剪误差与舍入误差, 导致模型性能明显下降. 为此, 提出一种面向低比特Transformer模型的无约束训练后量化方法(CFQuant), 通过建模神经网络激活值的概率分布实现自适应量化. 首先, CFQuant在校准过程中自适应估计激活分布密度, 并通过迭代搜索最小化量化误差. 其次, 设计高效尺度偏移算法动态调整模型分布, 以减小校准阶段与推理阶段之间的分布偏移, 进一步提升量化稳定性. 此外, 构建基于查找表的矩阵乘法加速机制, 将低比特推理中的浮点乘法转换为预计算查找操作, 从而降低推理计算开销.最后, 通过在多类Transformer模型以及视觉、语言和多模态任务上的大量实验, 充分验证了所提方法的灵活性和有效性.
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关键词:
- 深度学习 /
- 训练后量化 /
- Transformer /
- 量化误差 /
- 自注意力
Abstract: The massive parameter scales and high computational overhead of Transformer models make them difficult to deploy directly on resource-constrained edge devices, limiting their practical applications in open environments. Low-bit quantization can significantly reduce model storage requirements and improve inference efficiency, making it an important technical approach for lightweight deployment of Transformer models. However, existing quantization methods are usually constrained by fixed quantization intervals. When processing long-tailed distributions produced by nonlinear activations, they have difficulty balancing clipping and rounding errors effectively, leading to considerable performance degradation. To address this problem, we propose a constraint-free post-training quantization method for low-bit Transformer models (CFQuant), which performs adaptive quantization by modeling the probability distributions of neural-network activations. First, CFQuant adaptively estimates activation-distribution density during calibration and minimizes quantization error through iterative search. Second, an efficient scale-shift algorithm dynamically adjusts model distributions to reduce the distribution shift between calibration and inference stages, thereby further improving quantization stability. Moreover, an acceleration mechanism based on matrix multiplication with a lookup table converts floating-point multiplications in low-bit inference into precomputed lookup operations, thereby reducing inference overhead. Finally, extensive experiments on multiple types of Transformer models and on vision, language, and multimodal tasks demonstrate the flexibility and effectiveness of the proposed method.-
Key words:
- deep learning /
- post-training quantization /
- Transformer /
- quantization error /
- self-attention
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图 3 保留不同激活值为全精度的性能比较
Fig. 3 Performance comparison when different activations are retained at full precision
图 5 CFQuant对量化误差和模型性能的影响
Fig. 5 Effect of CFQuant on quantization error and model performance
图 6 不同校准样本数量下的Top-1准确率对比
Fig. 6 Top-1 accuracy comparison with different calibration sample sizes
表 1 不同方法在ImageNet-1k数据集上分类任务的性能对比(%)
Table 1 Performance comparison of different methods on classification tasks on ImageNet-1k dataset (%)
方法 比特数(W/A) ViT-T ViT-S ViT-B DeiT-T DeiT-S DeiT-B Swin-T Swin-S Swin-B 全精度 32/32 75.47 81.39 84.54 72.21 79.85 81.80 81.37 83.23 85.27 PTQ4ViT[19] 4/4 16.53 42.57 30.69 36.96 34.08 64.39 73.06 76.09 74.02 APQ-ViT[33] 4/4 17.56 47.95 41.41 47.94 43.55 67.48 — 77.15 76.48 RepQ-ViT[20] 4/4 26.72 65.05 68.48 57.43 69.03 75.61 72.37 79.45 80.74 CFQuant 4/4 55.41 70.95 73.72 62.57 72.57 78.02 73.80 80.65 81.84 
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表 2 不同方法在MS-COCO数据集上目标检测和实例分割任务的性能对比(%)
Table 2 Performance comparison of different methods on object detection and instance segmentation tasks on the MS-COCO dataset (%)
方法 比特数(W/A) Mask R-CNN Cascade Mask R-CNN Swin-T Swin-S Swin-T Swin-S 边界框AP 掩码AP 边界框AP 掩码AP 边界框AP 掩码AP 边界框AP 掩码AP 全精度 32/32 46.0 41.6 48.5 43.3 50.4 43.7 51.9 45.0 PTQ4ViT[19] 4/4 6.9 7.0 26.7 26.6 14.7 13.5 0.5 0.5 APQ-ViT[33] 4/4 23.7 22.6 44.7 40.1 27.2 24.4 47.7 41.1 RepQ-ViT[20] 4/4 36.1 36.0 44.2 40.2 47.0 41.4 49.3 43.1 CFQuant 4/4 36.6 36.5 43.4 40.6 47.7 42.0 50.1 43.6
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表 3 在多个零样本任务上LLaMA系列模型不同方法的性能对比(%)
Table 3 Performance comparison of different methods on multiple zero-shot tasks across LLaMA models (%)
模型 方法 比特数(W/A) PIQA ARC-e WinoGrande BoolQ ARC-c HellaSwag 平均值 LLaMA-7B 全精度 16/16 77.47 52.48 67.07 73.08 41.46 73.00 64.09 SmoothQuant[15] 4/4 49.80 30.40 48.00 49.10 25.80 27.40 38.41 OmniQuant[36] 4/4 66.15 45.20 53.43 63.51 31.14 56.44 52.65 AffineQuant[60] 4/4 69.37 42.55 55.33 63.73 31.91 57.65 53.42 CFQuant 4/4 67.91 43.90 55.36 64.45 32.19 57.14 53.49 LLaMA-13B 全精度 16/16 79.10 59.89 70.31 68.01 44.45 76.21 66.33 SmoothQuant[15] 4/4 61.04 39.18 51.06 61.80 30.80 52.29 49.36 OmniQuant[36] 4/4 69.69 47.39 55.80 62.84 33.10 58.96 54.63 AffineQuant[60] 4/4 66.32 43.90 54.70 64.10 29.61 56.88 52.58 CFQuant 4/4 71.20 45.61 56.39 64.17 33.35 59.51 55.04
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表 4 在多个零样本任务上Qwen3系列模型不同方法的性能对比(%)
Table 4 Performance comparison of different methods on multiple zero-shot tasks across Qwen3 models (%)
模型 方法 比特数(W/A) PIQA ARC-e WinoGrande BoolQ ARC-c HellaSwag 平均值 Qwen3-8B 全精度 16/16 77.80 80.93 67.72 86.61 56.66 74.92 74.11 SmoothQuant[15] 4/8 73.42 71.01 62.16 79.11 44.32 51.68 63.62 PrefixQuant[61] 4/8 71.98 70.50 64.09 82.26 46.93 65.09 66.81 CFQuant 4/8 76.17 71.13 65.82 79.79 47.61 71.56 68.68 SmoothQuant[15] 4/4 50.53 25.51 52.17 39.58 25.73 26.72 36.71 PrefixQuant[61] 4/4 56.42 38.55 48.07 45.69 26.79 34.82 41.72 CFQuant 4/4 72.74 71.84 64.09 78.81 47.87 67.93 67.21 Qwen3-14B 全精度 16/16 79.82 82.87 72.93 89.33 60.24 78.82 77.34 SmoothQuant[15] 4/4 51.22 25.81 50.18 38.47 26.51 25.79 36.33 PrefixQuant[61] 4/4 57.89 43.81 51.30 56.73 29.10 39.83 46.44 CFQuant 4/4 65.07 58.71 56.91 78.84 40.10 49.39 58.17
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表 5 在WikiText-2和C4数据集上语言生成任务的性能比较
Table 5 Performance comparison on language generation tasks on WikiText-2 and C4 datasets
模型 方法 比特数(W/A) WikiText-2 $ \downarrow $ C4 $ \downarrow $ LLaMA-7B 全精度 16/16 5.68 7.08 SmoothQuant[15] 4/4 25.25 32.32 OmniQuant[36] 4/4 11.26 14.51 CFQuant 4/4 10.36 13.91 LLaMA-13B 全精度 16/16 5.09 6.61 SmoothQuant[15] 4/4 40.05 47.18 OmniQuant[36] 4/4 10.87 13.78 CFQuant 4/4 10.14 13.28 Qwen3-8B 全精度 16/16 9.72 13.29 SmoothQuant[15] 4/4 $ 3.36\times10^{4} $ $ 2.29\times10^{4} $ PrefixQuant[61] 4/4 155.78 119.93 CFQuant 4/4 13.78 17.26 Qwen3-14B 全精度 16/16 8.64 12.01 SmoothQuant[15] 4/4 $ 2.16\times10^{5} $ $ 1.99\times10^{5} $ PrefixQuant[61] 4/4 187.28 129.05 CFQuant 4/4 32.30 35.76
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表 6 在MMBench数据集上Qwen3-VL-4B模型的 不同方法性能对比(%)
Table 6 Performance comparison of different methods for the Qwen3-VL-4B model on the MMBench dataset (%)
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表 7 在ImageNet-1k数据集上查找表额外内存开销的消融实验
Table 7 Ablation study of the additional lookup-table memory overhead on the ImageNet-1k dataset
模型 CFQuant 模型尺寸(MB) Top-1准确率(%) DeiT-S × 11.18 68.27 √ 11.19 (+0.1%) 72.57 (+4.30) Swin-S × 24.78 79.03 √ 24.80 (+0.2%) 80.65 (+1.62)
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表 8 在ImageNet-1k数据集上不同激活函数 量化策略的消融实验
Table 8 Ablation study of quantization strategies for different activation functions on the ImageNet-1k dataset
模型 Softmax GeLU Top-1准确率(%) DeiT-S × × 68.27 √ × 68.82 (+0.55) × √ 71.33 (+3.06) √ √ 72.57 (+4.30) Swin-S × × 79.03 √ × 79.28 (+0.25) × √ 80.36 (+1.33) √ √ 80.65 (+1.62)
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表 9 在ImageNet-1k数据集上高效尺度偏移算法的 消融实验
Table 9 Ablation studies of efficient scale-shift algorithm on the ImageNet-1k dataset
模型 ESA Top-1准确率(%) DeiT-S × 71.08 √ 72.57 (+1.49) Swin-S × 78.93 √ 80.65 (+1.72)
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表 10 在ImageNet-1k数据集上不同量化方法校准时间的对比
Table 10 Comparison of calibration time for different quantization methods on the ImageNet-1k dataset
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