GPTQ-2D: Cubic-Time Two-Sided Adaptive Rounding

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.

Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG)

arXiv:2607.27042 [cs.DS]

(or arXiv:2607.27042v1 [cs.DS] for this version)

https://doi.org/10.48550/arXiv.2607.27042 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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