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

• URL: http://arxiv.org/abs/2501.19090v1
• Date: Fri, 31 Jan 2025 12:36:31 GMT
• Title: Pivoting Factorization: A Compact Meta Low-Rank Representation of Sparsity for Efficient Inference in Large Language Models
• Authors: Jialin Zhao, Yingtao Zhang, Carlo Vittorio Cannistraci,
• Abstract summary: We present Pivoting Factorization (PIFA), a novel low-rank representation that unsupervisedly learns a compact form of any low-rank representation. To mitigate the performance degradation caused by low-rank pruning, we introduce a novel, retraining-free low-rank reconstruction method. MPIFA significantly outperforms existing low-rank pruning methods and, for the first time, achieves performance comparable to semi-structured pruning.
• Score: 1.6385815610837167
• License:
• 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 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 minimizes 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.

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