提出GPTQ-2D，用立方时间实现双侧自适应量化，速度更快且精度相同。
GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding
- 按反对角线顺序并行处理矩阵元素，避免逐个传递误差
- 在相同精度下，计算复杂度从四次方降至三次方
- 适合需要高效矩阵量化的大模型部署场景
自适应量化方法如GPTQ（等价于Babai最近平面算法）在二次度量下将实数矩阵舍入为整数。它们按固定顺序逐个处理元素，通过三角反馈矩阵将每次舍入误差传播至未处理的元素。本文研究该任务的双侧版本：左右各有一个固定非奇异基矩阵作用于残差矩阵；经典的一侧情况是右基为单位阵的特例。向量化后，双侧目标变为克罗内克积形式的二次度量，一维算法可直接应用，但时间复杂度为矩阵维度的四次方。我们提出GPTQ-2D，可在立方时间生成完全相同的量化结果。其按反对角线顺序处理元素，同一条反对角线上的元素相互独立，可并行量化。
原文摘要 · Abstract (English)
Adaptive rounding methods such as GPTQ, or equivalently Babai's nearest plane algorithm, round a real matrix to integers under a quadratic metric. They process the entries in a fixed order, one at a time, propagating each rounding error to the entries not yet processed through a triangular feedback matrix. We study the two-sided version of this task, in which fixed nonsingular basis matrices act on both the left and the right of the residual; the familiar one-sided case is the special case of an identity right basis. Vectorizing the matrix turns the two-sided objective into a quadratic metric whose Gram matrix is a Kronecker product, so the one-dimensional algorithm applies verbatim, but takes quartic time in the matrix dimension. We present GPTQ-2D, which produces the identical rounded matrix in cubic time. It rounds the entries anti-diagonal by anti-diagonal; entries on the same anti-diagonal are independent and are rounded in parallel.
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