Householder-Diagonalized Linear Attention (HDLA): Utilizing Enhanced Decay Mechanism for Efficient Sequence Modeling

Linear attention mechanisms have emerged as efficient alternatives to Softmax attention, exhibiting steady improvements in language modeling capabilities driven by increasingly sophisticated designs for decay matrices—though their structural complexity has typically been limited to the Diagonal-Plus-Rank-1 level. To further advance the understanding and capabilities of linear attention via more complex decay structures, this work makes two primary contributions: (1) We propose the HDLA linear attention mechanism, which utilizes efficient matrix decomposition to achieve a Diagonal-Plus-Rank-2 structure, thereby extending the decay matrix to a broader, more expressive, rank-enhanced and structured class. (2) We propose a more general chunk-wise parallel algorithm that accommodates both diagonal-plus-rank-$r_{ab}$ decay structure and key-value outer products of rank $r_{kv}$, thus providing a versatile foundation for future research. Comprehensive experiments demonstrate that, compared to linear attention baselines, HDLA sets new SOTA results on language modeling and retrieval tasks at 2.8B parameter scale, delivers at most 80\% and 58.2\% performance gains over baselines on retrieval-based MQAR and RULER tasks, and achieves an average score improvement of 4.39–7.66 on the synthetic MAD benchmark, respectively. Our proposed HDLA model, as well as the rank-generalized chunk-wise parallel algorithm, together provide a versatile algorithmic foundation and promising research prospects for the design of rank-enhanced, structured linear attention mechanisms.