Title: DBA: Efficient Transformer with Dynamic Bilinear Low-Rank Attention. Abstract: Many studies have been conducted to improve the efficiency of the Transformer from quadric to linear over long sequence conditions. Among them, the low-rank-based methods aim to learn the projection matrices to compress the sequence length, thus achieving efficiency gain. However, the projection matrices are fixed once they have been learned, which compress the sequence length with dedicated coefficients for the tokens in the same position regardless of different sequences. Adopting such input-invariant low-rank projections ignores the fact that the most informative part of a sequence varies from sequence to sequence, thus failing to preserve the most useful information that lies in varied positions of different sequences. In addition, previous efficient Transformers only focus on the influence of sequence length while neglecting the effect of hidden state dimension to achieve further efficiency gain. To address the aforementioned problems, we present an efficient yet effective attention mechanism, namely the Dynamic Bilinear Low-Rank Attention (DBA), which compresses the sequence length by input-sensitive dynamic projection matrices and achieves linear time and space complexity by jointly optimizing the sequence length and hidden state dimension while maintaining state-of-the-art performance. Specifically, we first theoretically demonstrate that the sequence length can be compressed non-destructively from a novel perspective of the information theory, with the compression matrices dynamically determined by the input sequence. Furthermore, we show that the hidden state dimension can be approximated by extending the Johnson–Lindenstrauss lemma and achieves high-order small amount error, optimizing the attention in bilinear form. In addition, theoretical analysis shows that the DBA is proficient in capturing high-order relations in cross-attention problems. Experiments over tasks with diverse sequence length conditions show that the DBA achieves state-of-the-art performance compared with various strong baselines while maintaining less memory consumption with higher speed, demonstrating the effectiveness and efficiency of the DBA.