The Lattice Geometry of Neural Network Quantization -- A Short Equivalence Proof of GPTQ and Babai's algorithm
This provides theoretical insight into quantization methods for neural networks, potentially enabling better compression techniques.
The paper shows that neural network quantization corresponds to solving the closest vector problem in lattice geometry, proving that GPTQ is equivalent to Babai's nearest-plane algorithm and suggesting lattice basis reduction could improve quantization.
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 for using lattice basis reduction for better quantization.