Large language models (LLMs) have achieved overwhelming success but require massive storage and computational resources to support the generative inference. Post-training quantization (PTQ) is a promising approach to reduce memory usage, latency and energy consumption of the deployment of LLMs. However, the presence of outliers makes most existing PTQ methods dedicated to dynamic quantization, which turns out hardware-unfriendly and often leads to large quantization errors in static scenarios. To address the above limitations, we introduce a Static Hierarchical Mix-precision Quantization method (SHMQ), which enables near-lossless and hardware-friendly compression of LLMs. Theoretically, our proposed SHMQ quantifies both inter-layer and intra-layer sensitivity through unified derivations involving Hessian. Specifically, SHMQ conducts a systematic precision allocation strategy, which seamlessly integrates coarse-grained inter-layer and fine-grained intra-layer static mix-precision quantization. Furthermore, the permutation procedure, which reorders sensitive channels and insensitive channels that share similar distribution, is leveraged to mitigate static quantization error. Our proposed SHMQ achieves 75.58% on zero-shot reasoning tasks in W4.8A8 Qwen2.5-7B-Instruct, narrowing the accuracy gap to merely 0.13% while yielding averaged 2.86× practical speedup.

Large Language Models (LLMs) have demonstrated remarkable proficiency in language comprehension and generation; however, their widespread adoption is constrained by substantial bandwidth and computational demands. While pruning and low-rank approximation have each demonstrated promising performance individually, their synergy for LLMs remains underexplored. We introduce Synergistic Sparse and Low-Rank Compression (SSLC) methods for LLMs, which leverages the strengths of both techniques: low-rank approximation compresses the model by retaining its essential structure with minimal information loss, whereas sparse optimization eliminates non-essential weights, preserving those crucial for generalization. Based on theoretical analysis, we first formulate the joint low-rank approximation and sparse optimization as a unified problem and solve it by iterative optimization algorithm. Experiments on LLaMA and Qwen2.5 models (7B-70B) show that SSLC, without any additional training steps, consistently surpasses standalone methods, achieving state-of-the-arts results. Notably, SSLC compresses Qwen2.5 by 50% with no performance drop and achieves at least 1.63× speedup, offering a practical solution for efficient LLM deployment.