# Tucker Attention: A generalization of approximate attention mechanisms

arXiv: https://arxiv.org/abs/2603.30033 · HTML: https://mlsanity.com/paper/2603.30033/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 31 Mar 2026.

## Builds on (most cited first, 14 of 14)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [Multi-Head Attention: Collaborate Instead of Concatenate](https://mlsanity.com/paper/2006.16362/) (2020)
- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [TransMLA: Multi-Head Latent Attention Is All You Need](https://mlsanity.com/paper/2502.07864/) (2025)
- [TensorLLM: Tensorising Multi-Head Attention for Enhanced Reasoning and Compression in LLMs](https://mlsanity.com/paper/2501.15674/) (2025)

## Built on by (most cited first, 3 of 3)

- [TEMPER: Tensorized Efficient Manifold-constrained Parameterization for Expressive Residual Routing](https://mlsanity.com/paper/2608.07851/) (2026)
- [Riemannian Gradient Descent for Low-Rank Architectures](https://mlsanity.com/paper/2606.02328/) (2026)
- [Tucker Bottleneck Attention for Multi-Dimensional Sequence Modeling](https://mlsanity.com/paper/2610.09090/) (2026)

## Abstract (arXiv)

The pursuit of reducing the memory footprint of the self-attention mechanism in multi-headed self attention (MHA) spawned a rich portfolio of methods, e.g., group-query attention (GQA) and multi-head latent attention (MLA). The methods leverage specialized low-rank factorizations across embedding dimensions or attention heads. From the point of view of classical low-rank approximation, these methods are unconventional and raise questions of which objects they really approximate and how to interpret the low-rank behavior of the resulting representations. To answer these questions, this work proposes a generalized view on the weight objects in the self-attention layer and a factorization strategy, which allows us to construct a parameter efficient scheme, called Tucker Attention. Tucker Attention requires an order of magnitude fewer parameters for comparable validation metrics, compared to GQA and MLA, as evaluated in LLM and ViT test cases. Additionally, Tucker Attention~encompasses GQA, MLA, MHA as special cases and is fully compatible with flash-attention and rotary position embeddings (RoPE). This generalization strategy yields insights of the actual ranks achieved by MHA, GQA, and MLA, and further enables simplifications for MLA.