  Quantization has become a crucial step for the efficient deployment of deep
neural networks, where floating point operations are converted to simpler fixed
point operations. In its most naive form, it simply consists in a combination
of scaling and rounding transformations, leading to either a limited
compression rate or a significant accuracy drop. Recently, Gradient-based
post-training quantization (GPTQ) methods appears to be constitute a suitable
trade-off between such simple methods and more powerful, yet expensive
Quantization-Aware Training (QAT) approaches, particularly when attempting to
quantize LLMs, where scalability of the quantization process is of paramount
importance. GPTQ essentially consists in learning the rounding operation using
a small calibration set. In this work, we challenge common choices in GPTQ
methods. In particular, we show that the process is, to a certain extent,
robust to a number of variables (weight selection, feature augmentation, choice
of calibration set). More importantly, we derive a number of best practices for
designing more efficient and scalable GPTQ methods, regarding the problem
formulation (loss, degrees of freedom, use of non-uniform quantization schemes)
or optimization process (choice of variable and optimizer). Lastly, we propose
a novel importance-based mixed-precision technique. Those guidelines lead to
significant performance improvements on all the tested state-of-the-art GPTQ
methods and networks (e.g. +6.819 points on ViT for 4-bit quantization), paving
the way for the design of scalable, yet effective quantization methods.
