Pruning is a critical strategy for compressing trained large language models (LLMs), aiming at substantial memory conservation and computational acceleration without compromising performance. However, existing pruning methods often necessitate inefficient retraining for billion-scale LLMs or rely on heuristic methods such as the optimal brain surgeon framework, which degrade performance. In this paper, we introduce FISTAPruner, the first post-training pruner based on convex optimization models and algorithms. Specifically, we propose a convex optimization model incorporating $\ell_1$ norm to induce sparsity and utilize the FISTA solver for optimization. FISTAPruner incorporates an intra-layer cumulative error correction mechanism and supports parallel pruning. We comprehensively evaluate FISTAPruner on models such as OPT, LLaMA, LLaMA-2, and LLaMA-3 with 125M to 70B parameters under unstructured and 2:4 semi-structured sparsity, demonstrating superior performance over existing state-of-the-art methods across various language benchmarks.

本研究解决了现有大型语言模型剪枝方法需要低效再训练或性能下降的问题。本文提出的FISTAPruner是首个基于凸优化的后训练剪枝器，采用$\ell_1$范数诱导稀疏性，并利用FISTA求解器进行优化。实验表明FISTAPruner在多种语言基准上相较于现有最先进方法表现更优。

基于凸优化的分层后训练剪枝方法用于大型语言模型