The Lattice Geometry of Neural Network Quantization: A Short Equivalence Proof of GPTQ and Babai's algorithm

ICLR 2026 Conference Submission21508 Authors

Keywords: quantization, lattices, GPTQ, Babai

TL;DR: We prove that the GPTQ quantization algorithm is equivalent to Babai's nearest-plane algorithm.

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.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 21508