arXiv:2609.08135cs.LGcs.AI2026-09

提出新型量化噪声模型,突破4比特浮点量化性能极限。

KBBQ: A Predictive Noise Law and the Limits of Spectrum Flattening in FP4 Quantization

  • 构建二阶量化噪声理论,用参与因子κ刻画噪声特性
  • 在W4A4下四模型两格式均超越当前最佳性能
  • 无需额外计算开销,适合部署于资源受限场景

我们建立了矩阵乘法中量化噪声的二阶理论,量化格式由各元素分配的方差表征。整数量化恒定方差特性恢复了已有整数噪声理论,而浮点舍入的乘性方差特性将数据依赖性简化为标量参与因子κ,推导出闭式信噪比公式。该函数还存在闭式上界κ*,任何保持函数性质的线性变换都无法超越,且已被最新先进方法实现。基于此分析,我们提出KBBQ(Kappa-Braked Blockwise Quantization),通过参数化变换逼近该理论上限。在W4A4配置下,覆盖四个基础模型和两种FP4格式,KBBQ在不增加部署时计算成本的前提下超越了先前最优方法。

原文摘要 · Abstract (English)

We develop a second-order theory of quantization noise in matrix multiplication in which the quantization format is characterized by the variance it assigns to each element. The constant variance profile of integer quantization recovers existing integer-noise theory, while the multiplicative profile of floating-point rounding reduces the data dependence to a scalar, the participation factor $\kappa$, yielding a closed-form signal-to-noise-ratio law. The resulting functional also admits a closed-form upper bound $\kappa^{*}$ that no function-preserving linear transform can exceed and that is attained by a recent state-of-the-art method. Building on this analysis, we introduce KBBQ (\textbf{K}appa-\textbf{B}raked \textbf{B}lockwise \textbf{Q}uantization), which parameterizes the extent to which a transform approaches this ceiling. At W4A4, across four base models and two FP4 formats, KBBQ outperforms the prior state of the art without additional deployment-time computation.

量化浮点量化噪声建模高效推理

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