Title: RCPU: Rotation-Constrained Error Compensation for Structured Pruning of a Large Language Model
Primary area: foundation or frontier models, including LLMs
Keywords: LLM, Compression, Pruning

Abstract: In this paper, we propose a rotation-constrained compensation method to address the errors introduced by structured pruning of large language models (LLMs). 
LLMs are trained on massive datasets and accumulate rich semantic knowledge in their representation space. 
In contrast, pruning is typically carried out with only a small amount of calibration data, which makes output mismatches unavoidable. 
Although direct least-squares fitting can reduce such errors, it tends to overfit to the limited calibration set, destructively modifying pretrained weights. 
To overcome this difficulty, we update the pruned parameters under a rotation constraint. 
This constrained update preserves the geometry of output representations (i.e., norms and inner products) and simultaneously re-aligns the pruned subspace with the original outputs.
Furthermore, in rotation-constrained compensation, removing components that strongly contribute to the principal directions of the output makes error recovery difficult. 
Since input dimensions with large variance strongly affect these principal directions, we design a variance-aware importance score that ensures such dimensions are preferentially kept in the pruned model. 
By combining this scoring rule with rotation-constrained updates, the proposed method effectively compensates errors while retaining the components likely to be more important in a geometry-preserving manner.
In the experiments, we apply the proposed method to LLaMA-7B and evaluate it on WikiText-2 and multiple language understanding benchmarks. 
The results demonstrate consistently better perplexity and task accuracy compared with existing baselines.
Codes are available at \url{https://anonymous.4open.science/r/anonymous-llm-pruning-D884/}