The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm
Machine Learning
2026-03-04 v2 Artificial Intelligence
Abstract
We explain how data-driven quantization of a linear unit in a neural network corresponds to solving the closest vector problem for a certain lattice generated by input data. We prove that the GPTQ algorithm is equivalent to Babai's well-known nearest-plane algorithm. We furthermore provide geometric intuition for both algorithms. Lastly, we note the consequences of these results, in particular hinting at the possibility of using lattice basis reduction for improved quantization.
Cite
@article{arxiv.2508.01077,
title = {The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm},
author = {Johann Birnick},
journal= {arXiv preprint arXiv:2508.01077},
year = {2026}
}
Comments
9 pages, 3 figures, accepted at ICLR 2026