Dynamic Low-rank Estimation for Transformer-based Language Models

Matrix decomposition methods, such as Singular Value Decomposition (SVD) and its importance-weighted variants, have been widely used for compressing Transformerbased language models. While importanceweighted decomposition methods alleviate the strong assumption of equal importance for each parameter in SVD, they still rely on two fundamental assumptions: 1) unchanged importance distribution during further fine-tuning, 2) equal importance across weight matrices in different layers. Furthermore, these methods necessitate a well-trained task-specific model as the starting point and require additional fine-tuning after compression. In this work, we proposed RankDyna, a matrix decomposition method that enables dynamic rank resource allocation among matrices across different layers during the training process. Starting from a general pre-trained model, RankDyna accomplishes the dual goals of compression and adaptation to the downstream task, all within a single round of fine-tuning. The extensive evaluations demonstrate that RankDyna can outperform current SOTA methods under various parameter budget levels, and the advantage of RankDyna is further enhanced with higher compression rates.