发表机构
Institute of Science and Technology Austria (ISTA); ETH Zürich; Red Hat AI（奥地利科学技术研究所（ISTA）; 苏黎世联邦理工学院; 红帽人工智能部门）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出GPTQ-2D算法，将原四次时间复杂度的双侧自适应舍入问题优化为三次时间，按反对角线并行舍入，保留与原算法相同的舍入结果。
AI 中文摘要
GPTQ等自适应舍入方法（等价于Babai最近平面算法）在二次度量下将实矩阵舍入为整数，按固定顺序逐个处理元素，通过三角反馈矩阵将每个舍入误差传播到未处理元素。本文研究该任务的双侧版本，其中固定非奇异基矩阵作用于残差的左右两侧，常见的单侧情况是右侧基为单位矩阵的特例。将矩阵向量化后，双侧目标变为Gram矩阵为克罗内克积的二次度量，一维算法可直接应用，但时间复杂度为矩阵维度的四次方。本文提出GPTQ-2D，可在三次时间内生成相同的舍入矩阵，按反对角线逐个处理元素，同一反对角线上的元素相互独立，可并行舍入。
英文摘要
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.
