AlphaPruning: Using Heavy-Tailed Self Regularization Theory for Improved Layer-wise Pruning of Large Language Models

Haiquan Lu, Yefan Zhou, Shiwei Liu, Zhangyang Wang, Michael W. Mahoney, Yaoqing Yang

Keywords: Pruning, large language models, heavy tails

TL;DR: We use methods derived from HT-SR Theory to develop improved methods for pruning LLMs.

Abstract: Recent work on pruning large language models (LLMs) has shown that one can eliminate a large number of parameters without compromising performance, making pruning a promising strategy to reduce LLM model size. Existing LLM pruning strategies typically assign uniform pruning ratios across layers, limiting overall pruning ability; and recent work on layerwise pruning of LLMs is often based on heuristics that can easily lead to suboptimal performance. In this paper, we leverage Heavy-Tailed Self-Regularization (HT-SR) Theory, in particular the shape of empirical spectral densities (ESDs) of weight matrices, to design improved layerwise pruning ratios for LLMs. Our analysis reveals a wide variability in how well-trained, and thus relatedly how prunable, different layers of an LLM are. Based on this, we propose AlphaPruning, which uses shape metrics to allocate layerwise sparsity ratios in a more theoretically-principled manner. AlphaPruning can be used in conjunction with multiple existing LLM pruning methods. Our empirical results show that AlphaPruning prunes LLaMA-7B to 80% sparsity while maintaining reasonable perplexity, marking a first in the literature on LLMs.

Primary Area: Deep learning architectures

Submission Number: 8088