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

2025/08/01 by Johann Birnick, Birnick, Johann · 1 citation
Computer Science · Engineering · #Neural Networks and Applications #Advanced Graph Neural Networks #Ferroelectric and Negative Capacitance Devices

paper · pdf · doi:10.48550/arxiv.2508.01077

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.

Citations

• The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm
• Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization
• GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers
• Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning

Cited by

• The Geometry of LLM Quantization: GPTQ as Babai's Nearest Plane Algorithm
• Qronos: Correcting the Past by Shaping the Future... in Post-Training Quantization
• Price of metric universality in vector quantization is at most 0.11 bit

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