  Large language models (LLMs) achieve remarkable performance in natural
language understanding but require substantial computation and memory
resources. Post-training quantization (PTQ) is a powerful compression technique
extensively investigated in LLMs. However, existing PTQ methods are still not
ideal in terms of accuracy and efficiency, especially with below 4 bit-widths.
Standard PTQ methods using group-wise quantization suffer difficulties in
quantizing LLMs accurately to such low-bit, but advanced methods remaining
high-precision weights element-wisely are hard to realize their theoretical
hardware efficiency. This paper presents a Salience-Driven Mixed-Precision
Quantization scheme for LLMs, namely SliM-LLM. The scheme exploits the salience
distribution of weights to determine optimal bit-width and quantizers for
accurate LLM quantization, while aligning bit-width partition to groups for
compact memory usage and fast integer inference. Specifically, the proposed
SliM-LLM mainly relies on two novel techniques: (1) Salience-Determined Bit
Allocation utilizes the clustering characteristics of salience distribution to
allocate the bit-widths of each group, increasing the accuracy of quantized
LLMs and maintaining the inference efficiency; (2) Salience-Weighted Quantizer
Calibration optimizes the parameters of the quantizer by considering the
element-wise salience within the group, balancing the maintenance of salient
information and minimization of errors. Comprehensive experiments show that
SliM-LLM significantly improves the accuracy of LLMs at ultra-low bits, e.g.,
2-bit LLaMA-7B achieves a 5.5-times memory-saving than original model on NVIDIA
A800 GPUs, and 48% decrease of perplexity compared to the state-of-the-art
gradient-free PTQ method. Moreover, SliM-LLM+, which is integrated from the
extension of SliM-LLM with gradient-based quantizers, further reduces
perplexity by 35.1%.
