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arXiv · 2501.19090

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

Jialin Zhao·Yingtao Zhang·Carlo Vittorio Cannistraci
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Abstract

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 GPU compatibility across all densities. However, low-rank pruning struggles to match the performance of semi-structured pruning, often doubling perplexity 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 24.2% additional memory savings and 24.6% faster inference over low-rank layers at rank = 50% of dimension. To mitigate the performance degradation caused by low-rank pruning, we introduce a novel, retraining-free reconstruction method that minimizes error accumulation (M). MPIFA, combining M and PIFA into an end-to-end framework, significantly outperforms existing low-rank pruning methods, and achieves performance comparable to semi-structured pruning, while surpassing it in GPU efficiency and compatibility. Our code is available at https://github.com/biomedical-cybernetics/pivoting-factorization.

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Jialin Zhao, Yingtao Zhang, Carlo Vittorio Cannistraci. 2025-08-13. Pivoting Factorization: A Compact Meta Low-Rank Representation of Sparsity for Efficient Inference in Large Language Models. https://arxiv.org/abs/2501.19090

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