| title | GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding |
|---|---|
| authors | Jiale Chen, Torsten Hoefler, Dan Alistarh |
| date | 2026-07-29 |
| venue | arXiv (preprint, not peer reviewed) |
| id | arXiv:2607.27042 |
| affiliation | IST Austria Distributed Algorithms and Systems Lab |
| upvotes | 8 (Hugging Face Daily Papers, 2026-11-01) |
| links | abs pdf hf |
| abstract | 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. |
cite
@misc{chen2026gptq,
title={GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding},
author={Jiale Chen and Torsten Hoefler and Dan Alistarh},
year={2026},
eprint={2607.27042},
archivePrefix={arXiv},
url={https://arxiv.org/abs/2607.27042}
}