Pivoting Factorization: A Compact Meta Low-Rank Representation of Sparsity for Efficient Inference in Large Language Models

The rapid growth of Large Language Models has driven demand for effective model compression techniques to reduce memory and computation costs. Low-rank pruning has gained attention for its tensor coherence and GPU compatibility across all densities. However, low-rank pruning has struggled to match the performance of semi-structured pruning, often doubling perplexity (PPL) at similar densities. In this paper, we propose Pivoting Factorization (**PIFA**), a novel **lossless** meta low-rank representation that unsupervisedly learns a compact form of any low-rank representation, effectively eliminating redundant information. PIFA identifies pivot rows (linearly independent rows) and expresses non-pivot rows as linear combinations, achieving an additional **24.2\%** memory savings and **24.6\%** faster inference over low-rank layers at $r/d = 0.5$, thereby significantly enhancing performance at the same density. To mitigate the performance degradation caused by low-rank pruning, we introduce a novel, retraining-free low-rank reconstruction method that \underline{m}inimizes error accumulation (**M**). **MPIFA**, combining M and PIFA into an end-to-end framework, significantly outperforms existing low-rank pruning methods and, for the first time, achieves performance comparable to semi-structured pruning, while surpassing it in GPU efficiency and compatibility.