Identifying Sensitive Weights via Post-quantization Integral
This work addresses the problem of inaccurate sensitivity estimation for LLM quantization, which is crucial for reducing serving costs, but it is incremental as it builds on existing quantization methods.
The paper tackles the inaccuracy of existing sensitivity metrics for post-training weight quantization in LLMs, which underestimate quantization's impact on loss by orders of magnitude, and proposes Post-quantization Integral (PQI) and ReQuant, resulting in a 2.66 perplexity gain on Llama 3.2 1B with QTIP.
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.