Low-rank decomposition serves as a promising compression paradigm for large language models, however, rank allocation remains challenging: manual rules lack generalizability, and learning-based approaches incur heavy computational overhead. To address these issues, we formulate global low-rank allocation as a sorting-and-truncation pipeline, and score each singular component via dual criteria: \textbf{Local} singular energy ratio that quantifies the intrinsic importance within the decomposed parameter matrix and \textbf{Global} functional importance (measured by input-output cosine similarity) that evaluates the functional significance of decomposed modules. We verify the strong correlation between high input-output cosine similarity and low effective rank through geometric interpretation and experimental validation. Furthermore, we propose rank-preserving fine-tuning, which performs direct LoRA tuning on decomposed weights and avoids extra information loss caused by re-truncation in conventional merging pipelines. Empirical results confirm that our method delivers sustained performance enhancements when combined with models featuring distinct decomposition schemes, model sizes and architectural designs, e.g. in one-shot compression without further fine-tuning, our method reduces perplexity by up to 50\% compared with uniform and heuristic allocation baselines. Code will be available at https://github.com/EIT-NLP/LLM-Pruning.

翻译：暂无翻译