Numerical Optimizations for Weighted Low-rank Estimation on Language Model

• URL: http://arxiv.org/abs/2211.09718v1
• Date: Wed, 2 Nov 2022 00:58:02 GMT
• Title: Numerical Optimizations for Weighted Low-rank Estimation on Language Model
• Authors: Ting Hua, Yen-Chang Hsu, Felicity Wang, Qian Lou, Yilin Shen, Hongxia Jin
• Abstract summary: Singular value decomposition (SVD) is one of the most popular compression methods that approximates a target matrix with smaller matrices. Standard SVD treats the parameters within the matrix with equal importance, which is a simple but unrealistic assumption. We show that our method can perform better than current SOTA methods in neural-based language models.
• Score: 73.12941276331316
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple but unrealistic assumption. The parameters of a trained neural network model may affect task performance unevenly, which suggests non-equal importance among the parameters. Compared to SVD, the decomposition method aware of parameter importance is the more practical choice in real cases. Unlike standard SVD, weighted value decomposition is a non-convex optimization problem that lacks a closed-form solution. We systematically investigated multiple optimization strategies to tackle the problem and examined our method by compressing Transformer-based language models. Further, we designed a metric to predict when the SVD may introduce a significant performance drop, for which our method can be a rescue strategy. The extensive evaluations demonstrate that our method can perform better than current SOTA methods in compressing Transformer-based language models.

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