这篇论文给了个新方法 GPTQ-2D，把矩阵两侧舍入的计算时间从 O(n⁴) 砍到 O(n³)，适合大规模机器学习模型量化。
GPTQ-2D 是一种新的两侧自适应舍入方法，扩展了 GPTQ 和 Babai 最近平面算法。它将两侧舍入的目标转化为 Kronecker 积的二次度量，原本需要矩阵维度的四次方时间。GPTQ-2D 逐反对角线进行舍入，同一反对角线上的条目可并行处理，将复杂度降至三次方时间。该方法在保持舍入质量的同时实现了显著加速。
GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding
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.