Singular Value Decomposition (SVD) or its weighted variants has significantly progressed in compressing language models. Previous works assume the same importance for all operations and assign the same number of ranks for different layers in a language model. However, such a uniform rank selection is sub-optimal since different operations (layers) have non-uniform demand in capacity. In other words, a desired SVD strategy should allocate more ranks for important operations and vice versa. However, a globally-optimized selection of ranks for neural networks is still an open problem, and this is a non-trivial challenge since the selection is discrete. In this work, we propose a novel binary masking mechanism for optimizing the number of ranks in a differentiable framework. Our strategy uses a novel regularization to enable the masking to comply with the SVD property where the ranks have sorted singular values. The experiments examined both types of language models, encoder-only and decoder-only models, including large language models like LLaMA. Our compressed model achieves much better accuracy than previous SVD and their SOTA variants. More interestingly, our method retains significantly better accuracy with zero or limited fine-tuning, proving the substantial advantage of adaptive rank selection.

Matrix decomposition methods, such as Singular Value Decomposition (SVD) and its importance-weighted variants, have been widely used for compressing Transformer-based language models. While importance-weighted 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.