# Eigen Attention: Attention in Low-Rank Space for KV Cache Compression

arXiv: https://arxiv.org/abs/2408.05646 · HTML: https://mlsanity.com/paper/2408.05646/

## Key facts

- Cited by 72 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 44 references that are in the map.
- First posted on arXiv 10 Aug 2024.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)
- Efficient LLM inference and serving / [KV cache optimization](https://mlsanity.com/inference/kv-cache-optimization/)

## Builds on (most cited first, 27 of 27)

- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [GEAR: An Efficient KV Cache Compression Recipe for Near-Lossless Generative Inference of LLM](https://mlsanity.com/paper/2403.05527/) (2024)
- [Keyformer: KV Cache Reduction through Key Tokens Selection for Efficient Generative Inference](https://mlsanity.com/paper/2403.09054/) (2024)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [Long Context Compression with Activation Beacon](https://mlsanity.com/paper/2401.03462/) (2024)
- [No Token Left Behind: Reliable KV Cache Compression via Importance-Aware Mixed Precision Quantization](https://mlsanity.com/paper/2402.18096/) (2024)
- [LORD: Low Rank Decomposition Of Monolingual Code LLMs For One-Shot Compression](https://mlsanity.com/paper/2309.14021/) (2023)
- [ATP: Enabling Fast LLM Serving via Attention on Top Principal Keys](https://mlsanity.com/paper/2403.02352/) (2024)

## Built on by (most cited first, 30 of 72)

- [ShadowKV: KV Cache in Shadows for High-Throughput Long-Context LLM Inference](https://mlsanity.com/paper/2410.21465/) (2024)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [Cartridges: Lightweight and general-purpose long context representations via self-study](https://mlsanity.com/paper/2506.06266/) (2025)
- [R-KV: Redundancy-aware KV Cache Compression for Reasoning Models](https://mlsanity.com/paper/2505.24133/) (2025)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)
- [Tensor Product Attention Is All You Need](https://mlsanity.com/paper/2501.06425/) (2025)
- [MatryoshkaKV: Adaptive KV Compression via Trainable Orthogonal Projection](https://mlsanity.com/paper/2410.14731/) (2024)
- [Inference-Time Hyper-Scaling with KV Cache Compression](https://mlsanity.com/paper/2506.05345/) (2025)
- [Dialogue Without Limits: Constant-Sized KV Caches for Extended Responses in LLMs](https://mlsanity.com/paper/2503.00979/) (2025)
- [Cache What Lasts: Token Retention for Memory-Bounded KV Cache in LLMs](https://mlsanity.com/paper/2512.03324/) (2025)
- [xKV: Cross-Layer KV-Cache Compression via Aligned Singular Vector Extraction](https://mlsanity.com/paper/2503.18893/) (2025)
- [ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration](https://mlsanity.com/paper/2505.24357/) (2025)
- [KV Cache Transform Coding for Compact Storage in LLM Inference](https://mlsanity.com/paper/2511.01815/) (2025)
- [SALS: Sparse Attention in Latent Space for KV cache Compression](https://mlsanity.com/paper/2510.24273/) (2025)
- [STAR-KV: Low-Rank KV Cache Compression via Soft Thresholding for Adaptive Rank Control](https://mlsanity.com/paper/2606.08382/) (2026)
- [Hardware-Efficient Attention for Fast Decoding](https://mlsanity.com/paper/2505.21487/) (2025)
- [KVLinC : KV Cache Quantization with Hadamard Rotation and Linear Correction](https://mlsanity.com/paper/2510.05373/) (2025)
- [KQ-SVD: Compressing the KV Cache with Provable Guarantees on Attention Fidelity](https://mlsanity.com/paper/2512.05916/) (2025)
- [ResidualKV: Residual-Based KV Cache Compression for Efficient Long-Context Inference](https://mlsanity.com/paper/2602.08005/) (2026)
- [MixKVQ: Query-Aware Mixed-Precision KV Cache Quantization for Long-Context Reasoning](https://mlsanity.com/paper/2512.19206/) (2025)
- [FASA: Frequency-aware Sparse Attention](https://mlsanity.com/paper/2602.03152/) (2026)
- [Value-Aware Stochastic KV Cache Eviction for Reasoning Models](https://mlsanity.com/paper/2606.03928/) (2026)
- [LatentLLM: Attention-Aware Joint Tensor Compression](https://mlsanity.com/paper/2505.18413/) (2025)
- [OjaKV: Context-Aware Online Low-Rank KV Cache Compression](https://mlsanity.com/paper/2509.21623/) (2025)
- [SVDq: 1.25-bit and 410x Key Cache Compression for LLM Attention](https://mlsanity.com/paper/2502.15304/) (2025)
- [FlowKV: Enhancing Multi-Turn Conversational Coherence in LLMs via Isolated Key-Value Cache Management](https://mlsanity.com/paper/2505.15347/) (2025)
- [KV-Latent: Dimensional-level KV Cache Reduction with Frequency-aware Rotary Positional Embedding](https://mlsanity.com/paper/2507.11273/) (2025)
- [SAW-INT4: System-Aware 4-Bit KV-Cache Quantization for Real-World LLM Serving](https://mlsanity.com/paper/2604.19157/) (2026)
- [XQuant: Breaking the Memory Wall for LLM Inference with KV Cache Rematerialization](https://mlsanity.com/paper/2508.10395/) (2025)
- [NOSA: Native and Offloadable Sparse Attention](https://mlsanity.com/paper/2510.13602/) (2025)

## Abstract (arXiv)

Large language models (LLMs) represent a groundbreaking advancement in the domain of natural language processing due to their impressive reasoning abilities. Recently, there has been considerable interest in increasing the context lengths for these models to enhance their applicability to complex tasks. However, at long context lengths and large batch sizes, the key-value (KV) cache, which stores the attention keys and values, emerges as the new bottleneck in memory usage during inference. To address this, we propose Eigen Attention, which performs the attention operation in a low-rank space, thereby reducing the KV cache memory overhead. Our proposed approach is orthogonal to existing KV cache compression techniques and can be used synergistically with them. Through extensive experiments over OPT, MPT, and Llama model families, we demonstrate that Eigen Attention results in up to 40% reduction in KV cache sizes and up to 60% reduction in attention operation latency with minimal drop in performance. Code is available at https://github.com/UtkarshSaxena1/EigenAttn.