DBA: Efficient Transformer With Dynamic Bilinear Low-Rank Attention

Many studies have aimed to improve Transformer model efficiency using low-rank-based methods that compress sequence length with predetermined or learned compression matrices. However, these methods fix compression coefficients for tokens in the same position during inference, ignoring sequence-specific variations. They also overlook the impact of hidden state dimensions on efficiency gains. To address these limitations, we propose dynamic bilinear low-rank attention (DBA), an efficient and effective attention mechanism that compresses sequence length using input-sensitive dynamic compression matrices. DBA achieves linear time and space complexity by jointly optimizing sequence length and hidden state dimension while maintaining state-of-the-art performance. Specifically, we demonstrate through experiments and the properties of low-rank matrices that sequence length can be compressed with compression coefficients dynamically determined by the input sequence. In addition, we illustrate that the hidden state dimension can be approximated by extending the Johnson-Lindenstrauss lemma, thereby introducing only a small amount of error. DBA optimizes the attention mechanism through bilinear forms that consider both the sequence length and hidden state dimension. Moreover, the theoretical analysis substantiates that DBA excels at capturing high-order relationships in cross-attention problems. Experimental results across different tasks with varied sequence length conditions demonstrate that DBA achieves state-of-the-art performance compared to several robust baselines. DBA also maintains higher processing speed and lower memory usage, highlighting its efficiency and effectiveness across diverse applications.