[2508.01077] The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm

Computer Science > Machine Learning arXiv:2508.01077 (cs) [Submitted on 1 Aug 2025 (v1), last revised 2 Mar 2026 (this version, v2)] Title:The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm Authors:Johann Birnick View a PDF of the paper titled The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's Algorithm, by Johann Birnick View PDF HTML (experimental) 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. Comments: Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) ACM classes: I.2.6 Cite as: arXiv:2508.01077 [cs.LG]   (or arXiv:2508.01077v2 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2508.01077 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Johann Birnick [view email] [v1] Fri, 1 Aug 2025 21:20:58 UTC (124 KB) [v2] Mon, 2 Mar 2026 22:23:15 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled The Lattice Geometry of Neural Network Quantization -- A Short Eq...