# KQ-SVD: Compressing the KV Cache with Provable Guarantees on Attention Fidelity

arXiv: https://arxiv.org/abs/2512.05916 · HTML: https://mlsanity.com/paper/2512.05916/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in KV cache optimization, one of 12 directions in Efficient LLM inference and serving.
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [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)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [ShadowKV: KV Cache in Shadows for High-Throughput Long-Context LLM Inference](https://mlsanity.com/paper/2410.21465/) (2024)
- [Keep the Cost Down: A Review on Methods to Optimize LLM' s KV-Cache Consumption](https://mlsanity.com/paper/2407.18003/) (2024)
- [Loki: Low-rank Keys for Efficient Sparse Attention](https://mlsanity.com/paper/2406.02542/) (2024)
- [Eigen Attention: Attention in Low-Rank Space for KV Cache Compression](https://mlsanity.com/paper/2408.05646/) (2024)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [LoRC: Low-Rank Compression for LLMs KV Cache with a Progressive Compression Strategy](https://mlsanity.com/paper/2410.03111/) (2024)
- [Challenges in Deploying Long-Context Transformers: A Theoretical Peak Performance Analysis](https://mlsanity.com/paper/2405.08944/) (2024)
- [Sparse Attention with Linear Units](https://mlsanity.com/paper/2104.07012/) (2021)
- [Effectively Compress KV Heads for LLM](https://mlsanity.com/paper/2406.07056/) (2024)
- [Beyond Adult and COMPAS: Fairness in Multi-Class Prediction](https://mlsanity.com/paper/2206.07801/) (2022)
- [SQuat: Subspace-orthogonal KV Cache Quantization](https://mlsanity.com/paper/2503.24358/) (2025)

## Built on by (most cited first, 10 of 10)

- [Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold](https://mlsanity.com/paper/2601.21686/) (2026)
- [WitCert: Sound Runtime Risk Observability and Gating for KV-Cache Quantization](https://mlsanity.com/paper/2607.28699/) (2026)
- [Attention-Weighted Value Projection for KV-Cache Compression](https://mlsanity.com/paper/2604.11501/) (2026)
- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [KV-COBRA: KV Cache Compression via Co-Optimized Bit-Rank Allocation](https://mlsanity.com/paper/2609.24298/) (2026)
- [From Tensor Buffer to Distributed Memory Hierarchy: A Survey of KV Cache Management for LLM Serving](https://mlsanity.com/paper/2607.02574/) (2026)
- [A JoLT for the KV cache: Near-Lossless KV Cache Compression via Joint Rank-bit Allocation](https://mlsanity.com/paper/2607.12550/) (2026)
- [AttSVD:Prompt-Adaptive Low-Rank KV Cache Compression via Attention-Guided SVD](https://mlsanity.com/paper/2610.06927/) (2026)
- [Freeze the Decoder, Heal the Encoder: Parameter-Efficient Adaptation for SVD-Based KV-Cache Compression](https://mlsanity.com/paper/2610.10552/) (2026)
- [Joint Subspace Sparse Attention for Efficient Long-Context Decoding](https://mlsanity.com/paper/2610.19026/) (2026)

## Abstract (arXiv)

The Key-Value (KV) cache is central to the efficiency of transformer-based large language models (LLMs), storing previously computed vectors to accelerate inference. Yet, as sequence length and batch size grow, the cache becomes a major memory bottleneck. Prior compression methods typically apply low-rank decomposition to keys alone or attempt to jointly embed queries and keys, but both approaches neglect that attention fundamentally depends on their inner products. In this work, we prove that such strategies are suboptimal for approximating the attention matrix. We introduce KQ-SVD, a simple and computationally efficient method that directly performs an optimal low-rank decomposition of the attention matrix via a closed-form solution. By targeting the true source of redundancy, KQ-SVD preserves attention outputs with higher fidelity under compression. Extensive evaluations on LLaMA and Mistral models demonstrate that our approach consistently delivers superior projection quality.