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

TL;DR

This paper reveals the geometric relationship between neural network quantization and lattice problems, proving GPTQ's equivalence to Babai's algorithm and suggesting lattice basis reduction for better quantization.

Contribution

It establishes the equivalence between GPTQ and Babai's algorithm, providing geometric insights and proposing lattice basis reduction to enhance neural network quantization.

Findings

GPTQ is equivalent to Babai's nearest-plane algorithm

Provides geometric intuition for quantization algorithms

Suggests lattice basis reduction for improved quantization

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.