# Multi-matrix Factorization Attention

arXiv: https://arxiv.org/abs/2412.19255 · HTML: https://mlsanity.com/paper/2412.19255/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- First posted on arXiv 26 Dec 2024.

## Placed in

- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Built on by (most cited first, 6 of 6)

- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [SAS: Simulated Attention Score](https://mlsanity.com/paper/2507.07694/) (2025)
- [Low-Rank Key Value Attention](https://mlsanity.com/paper/2601.11471/) (2026)
- [Multi-Head Low-Rank Attention](https://mlsanity.com/paper/2603.02188/) (2026)
- [UHD Image Dehazing via anDehazeFormer with Atmospheric-aware KV Cache](https://mlsanity.com/paper/2505.14010/) (2025)
- [Virtual Head Attention](https://mlsanity.com/paper/2610.17959/) (2026)

## Abstract (arXiv)

We propose novel attention architectures, Multi-matrix Factorization Attention (MFA) and MFA-Key-Reuse (MFA-KR). Existing variants for standard Multi-Head Attention (MHA), including SOTA methods like MLA, fail to maintain as strong performance under stringent Key-Value cache (KV cache) constraints. MFA enhances model capacity by efficiently scaling up both the number and dimension of attention heads through low-rank matrix factorization in the Query-Key (QK) circuit. Extending MFA, MFA-KR further reduces memory requirements by repurposing the key cache as value through value projection re-parameterization. MFA's design enables strong model capacity when working under tight KV cache budget, while MFA-KR is suitable for even harsher KV cache limits with minor performance trade-off. Notably, in our extensive and large-scale experiments, the proposed architecture outperforms MLA and performs comparably to MHA, while reducing KV cache usage by up to 56% and 93.7%, respectively.