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

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 5.6Download Report PDF
Linear AttentionLanguage ModelFoundation Model
Abstract:

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-rabr_{ab} decay structure and key-value outer products of rank rkvr_{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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes HDLA, a linear attention mechanism employing a Diagonal-Plus-Rank-2 decay structure via Householder-based matrix decomposition, alongside a generalized chunk-wise parallel algorithm. Within the taxonomy, it resides in the 'Diagonal-Plus-Rank Decay Mechanisms' leaf under 'Rank-Enhanced Decay Structures for Linear Attention'. Notably, this leaf contains only the original paper itself—no sibling papers are present—indicating a relatively sparse research direction focused specifically on diagonal-plus-rank decay parameterizations with efficient decomposition techniques.

The taxonomy reveals that the broader 'Rank-Enhanced Decay Structures' branch includes a sibling leaf, 'Rank Augmentation for Attention Matrix Enhancement', which houses four papers addressing low-rank bottlenecks through rank augmentation strategies. These neighboring works (e.g., Breaking Low-Rank Dilemma, Raising Attention Rank) share the goal of enriching attention expressiveness but do not explicitly employ structured decay matrices. Meanwhile, the 'Low-Rank Approximation Methods' branch encompasses pure compression techniques like Linformer and LoLA, which lack decay structures entirely. HDLA's structured decay approach thus diverges from both pure low-rank compression and rank-augmentation-only methods, occupying a distinct niche.

Among the three contributions analyzed, the literature search examined four candidate papers total, identifying one refutable pair for the 'Householder-diagonalized decay parameterization with efficiency constraints' contribution. The other two contributions—HDLA's Diagonal-Plus-Rank-2 structure and the rank-generalized chunk-wise algorithm—were examined against zero candidates, suggesting limited prior work directly addressing these specific technical innovations within the scope of the top-K semantic search. This indicates that, among the small set of candidates reviewed, the core HDLA mechanism and parallel algorithm appear relatively unexplored, while the Householder parameterization has at least one overlapping prior work.

Given the limited search scope (four candidates examined), the analysis suggests HDLA introduces technical novelty in structured decay design and parallel computation, though the Householder parameterization component has identifiable prior overlap. The sparse taxonomy leaf and absence of sibling papers further imply that diagonal-plus-rank decay mechanisms remain an underexplored direction. However, the small candidate pool means the assessment reflects only a narrow slice of the literature, and a broader search could reveal additional related work.

Taxonomy

Core-task Taxonomy Papers
10
3
Claimed Contributions
4
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: Efficient sequence modeling with rank-enhanced structured linear attention mechanisms. The field addresses the computational bottleneck of standard softmax attention by exploring linear-time alternatives that preserve modeling capacity. The taxonomy reveals four main branches: Rank-Enhanced Decay Structures for Linear Attention, which incorporates structured decay patterns (often diagonal-plus-rank forms) to enrich expressiveness; Low-Rank Approximation Methods, which compress attention matrices through techniques like projection-based factorization (e.g., Linformer[1]) or low-rank parameterizations (e.g., LoLA[2]); Hybrid Attention Architectures, which blend linear and softmax mechanisms to balance efficiency and performance; and Domain-Specific Applications, which tailor these methods to tasks such as recommendation systems (MLSA4Rec[3]) or vision transformers (ViTALiTy[4]). These branches collectively aim to reduce quadratic complexity while maintaining or enhancing the rank and expressiveness of attention. Recent work has intensified around breaking the low-rank bottleneck inherent in many linear attention schemes. Several studies (Breaking Low-Rank Dilemma[10], Raising Attention Rank[8]) explicitly target rank augmentation to recover lost modeling power, while others introduce dual-stream or solver-based designs (Dual-Linear Attention[7], Rank-Augmented Solver[9]) to enrich feature interactions. Householder Diagonalized Attention[0] sits within the Rank-Enhanced Decay Structures branch, specifically under Diagonal-Plus-Rank Decay Mechanisms, where it leverages Householder transformations to diagonalize and augment decay structures. This approach contrasts with purely low-rank methods like Linformer[1] or LoLA[2], which compress without explicit decay modeling, and differs from domain-specific adaptations like Sla-former[5] that prioritize task-specific inductive biases. By combining structured decay with rank enhancement, Householder Diagonalized Attention[0] addresses both efficiency and expressiveness, positioning itself among works that seek principled ways to enrich linear attention beyond naive low-rank approximations.

Claimed Contributions

HDLA linear attention mechanism with Diagonal-Plus-Rank-2 decay structure

The authors introduce HDLA, a linear attention mechanism that employs generalized Householder matrices to diagonalize the decay matrix, achieving a Diagonal-Plus-Rank-2 structure. This extends beyond prior work limited to Diagonal-Plus-Rank-1 decay, providing a more expressive decay mechanism while maintaining parameter, memory, and computational efficiency.

0 retrieved papers
Rank-generalized chunk-wise parallel algorithm for linear attention

The authors develop a generalized chunk-wise parallel algorithm that simultaneously handles arbitrary diagonal-plus-rank-rab decay structures and rank-rkv key-value updates. This algorithmic framework subsumes HDLA as a special case and provides a foundation for future linear attention research with rank-enhanced structures.

0 retrieved papers
Householder-diagonalized decay parameterization with efficiency constraints

The authors propose a novel parameterization approach using congruence diagonalization theory and generalized Householder matrices to construct the decay matrix. They establish three efficiency constraints (parameter, memory, and computational) and demonstrate that their approach satisfies these constraints while achieving a Diagonal-Plus-Rank-2 structure.

4 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

HDLA linear attention mechanism with Diagonal-Plus-Rank-2 decay structure

The authors introduce HDLA, a linear attention mechanism that employs generalized Householder matrices to diagonalize the decay matrix, achieving a Diagonal-Plus-Rank-2 structure. This extends beyond prior work limited to Diagonal-Plus-Rank-1 decay, providing a more expressive decay mechanism while maintaining parameter, memory, and computational efficiency.

Contribution

Rank-generalized chunk-wise parallel algorithm for linear attention

The authors develop a generalized chunk-wise parallel algorithm that simultaneously handles arbitrary diagonal-plus-rank-rab decay structures and rank-rkv key-value updates. This algorithmic framework subsumes HDLA as a special case and provides a foundation for future linear attention research with rank-enhanced structures.

Contribution

Householder-diagonalized decay parameterization with efficiency constraints

The authors propose a novel parameterization approach using congruence diagonalization theory and generalized Householder matrices to construct the decay matrix. They establish three efficiency constraints (parameter, memory, and computational) and demonstrate that their approach satisfies these constraints while achieving a Diagonal-Plus-Rank-2 structure.

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