Identifying Sensitive Weights via Post-quantization Integral
Authors: name: Yuezhou Hu, name: Weiyu Huang, name: Zichen Liang, name: Chang Chen, name: Jintao Zhang, name: Jun Zhu, name: Jianfei Chen

Serving Large Language Models (LLMs) is costly. However, post-training weight
quantization can address this problem by both compressing their sizes for
limited memory and saving bandwidth for acceleration. As not all weight
dimensions are equally important, those methods typically rely on a sensitivity
metric, which indicates the element-wise influence of weights on loss function
and is used to preprocess original weights for better quantization. In this
work, we conduct an empirical study on the accuracy of the sensitivity metric,
and find that existing gradient and Hessian based metrics are very inaccurate:
they underestimate quantization's impact on the loss function by orders of
magnitude, mainly due to the small convergence radius of local 2nd order
approximation, \ie, gradient and Hessian term in Taylor's formula. To tackle
this problem, we propose Post-quantization Integral (PQI), an accurate metric
to estimate posterior sensitivity in a fine-grained manner. To leverage this
accurate metric, we further propose ReQuant, a simple yet powerful framework
that mainly consists of two Dense-and-Sparse detach components: self-adaptive
outlier selection and step-wise significant weights detach. Results show that
ReQuant boosts state-of-the-art post-training quantization methods, with a
pronounced improvement of 2.66 perplexity gain on Llama 3.2 1B with QTIP.