# Kronecker Product Attention: Memory-Efficient KV Compression via Structured Factorization

arXiv: https://arxiv.org/abs/2610.12657 · HTML: https://mlsanity.com/paper/2610.12657/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 28 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 24 of 24)

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [Kronecker Decomposition for GPT Compression](https://mlsanity.com/paper/2110.08152/) (2021)

## Abstract (arXiv)

Efficient autoregressive generation is increasingly limited by the memory footprint of the key-value (KV) cache, which grows linearly with sequence length, batch size, and model depth. Existing approaches such as Multi-Query Attention (MQA), Grouped-Query Attention (GQA), Multi-Head Latent Attention (MLA), and Tensor Product Attention (TPA) reduce this cost through different trade-offs, but often sacrifice expressivity, require additional positional-encoding machinery, or impose restrictive low-rank structure. We propose Kronecker Product Attention (KPA), which represents key and value activations as sums of Kronecker products of compact, token-dependent matrix factors. KPA strictly generalizes TPA: rank-one vector-outer-product factorization arises as a degenerate Kronecker split, while non-degenerate matrix factors can represent richer block-structured patterns. We further show that a structured rotary embedding operator matched to the Kronecker representation preserves the relative-position property of RoPE while rotating only the compact factors, removing the need for a decoupled RoPE branch as in MLA. Empirically, KPA matches or exceeds TPA, MHA, MQA, GQA, and MLA across four model scales and nine downstream benchmarks under identical training conditions, while achieving up to 10x KV cache compression. The Kronecker head split is a tuneable hyperparameter that allows practitioners to navigate the compression-accuracy trade-off at design time without architectural changes.