# MatryoshkaKV: Adaptive KV Compression via Trainable Orthogonal Projection

arXiv: https://arxiv.org/abs/2410.14731 · HTML: https://mlsanity.com/paper/2410.14731/

## Key facts

- Cited by 29 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 32 of its 42 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Placed in

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

## Builds on (most cited first, 30 of 32)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [A Comprehensive Overview of Large Language Models](https://mlsanity.com/paper/2307.06435/) (2023)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [LongRoPE: Extending LLM Context Window Beyond 2 Million Tokens](https://mlsanity.com/paper/2402.13753/) (2024)
- [Matryoshka Representation Learning](https://mlsanity.com/paper/2205.13147/) (2022)
- [Sentiment Analysis in the Era of Large Language Models: A Reality Check](https://mlsanity.com/paper/2305.15005/) (2023)
- [InfiniGen: Efficient Generative Inference of Large Language Models with Dynamic KV Cache Management](https://mlsanity.com/paper/2406.19707/) (2024)
- [Retrieval Head Mechanistically Explains Long-Context Factuality](https://mlsanity.com/paper/2404.15574/) (2024)
- [Continual Pre-training of Language Models](https://mlsanity.com/paper/2302.03241/) (2023)
- [Data Engineering for Scaling Language Models to 128K Context](https://mlsanity.com/paper/2402.10171/) (2024)
- [ASVD: Activation-aware Singular Value Decomposition for Compressing Large Language Models](https://mlsanity.com/paper/2312.05821/) (2023)
- [You Only Cache Once: Decoder-Decoder Architectures for Language Models](https://mlsanity.com/paper/2405.05254/) (2024)
- [Reducing Transformer Key-Value Cache Size with Cross-Layer Attention](https://mlsanity.com/paper/2405.12981/) (2024)
- [Keep the Cost Down: A Review on Methods to Optimize LLM' s KV-Cache Consumption](https://mlsanity.com/paper/2407.18003/) (2024)
- [Model Tells You Where to Merge: Adaptive KV Cache Merging for LLMs on Long-Context Tasks](https://mlsanity.com/paper/2407.08454/) (2024)
- [Eigen Attention: Attention in Low-Rank Space for KV Cache Compression](https://mlsanity.com/paper/2408.05646/) (2024)

## Built on by (most cited first, 29 of 29)

- [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)
- [ResQ: Mixed-Precision Quantization of Large Language Models with Low-Rank Residuals](https://mlsanity.com/paper/2412.14363/) (2024)
- [ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration](https://mlsanity.com/paper/2505.24357/) (2025)
- [STAR-KV: Low-Rank KV Cache Compression via Soft Thresholding for Adaptive Rank Control](https://mlsanity.com/paper/2606.08382/) (2026)
- [OSCAR: Offline Spectral Covariance-Aware Rotation for 2-bit KV Cache Quantization](https://mlsanity.com/paper/2605.17757/) (2026)
- [NSNQuant: A Double Normalization Approach for Calibration-Free Low-Bit Vector Quantization of KV Cache](https://mlsanity.com/paper/2505.18231/) (2025)
- [Mustafar: Promoting Unstructured Sparsity for KV Cache Pruning in LLM Inference](https://mlsanity.com/paper/2505.22913/) (2025)
- [OjaKV: Context-Aware Online Low-Rank KV Cache Compression](https://mlsanity.com/paper/2509.21623/) (2025)
- [MoME: Mixture of Matryoshka Experts for Audio-Visual Speech Recognition](https://mlsanity.com/paper/2510.04136/) (2025)
- [KV Admission: Learning What to Write for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2512.17452/) (2025)
- [Don't be so Stief! Learning KV Cache low-rank approximation over the Stiefel manifold](https://mlsanity.com/paper/2601.21686/) (2026)
- [RAP: KV-Cache Compression via RoPE-Aligned Pruning](https://mlsanity.com/paper/2602.02599/) (2026)
- [Cartridges++: KV Cache Compression without Off-Context Derailment](https://mlsanity.com/paper/2609.35621/) (2026)
- [TPLA: Tensor Parallel Latent Attention for Efficient Disaggregated Prefill and Decode Inference](https://mlsanity.com/paper/2508.15881/) (2025)
- [Hyperspectral Image Fusion with Spectral-Band and Fusion-Scale Agnosticism](https://mlsanity.com/paper/2602.01681/) (2026)
- [KV-Kaizen: Learning Context-Adaptive Cache Compression Choices](https://mlsanity.com/paper/2609.37988/) (2026)
- [Variance Is Not Importance: Structural Analysis of Transformer Compressibility Across Model Scales](https://mlsanity.com/paper/2604.20682/) (2026)
- [Rotation-Aligned Key Channel Pruning for Efficient Vision-Language Model Inference](https://mlsanity.com/paper/2605.19218/) (2026)
- [Beyond the Literal: Decomposing Pragmatic Intent in Multimodal Meme Understanding](https://mlsanity.com/paper/2606.03604/) (2026)
- [Dual Dimensionality for Local and Global Attention](https://mlsanity.com/paper/2606.18587/) (2026)
- [VarRate: Training-Free Variable-Rate KV Cache Compression for Long-Context LLMs](https://mlsanity.com/paper/2607.15498/) (2026)
- [Codec-Gauge: Learning Compression-Friendly Gauges for Transformer KV Caches](https://mlsanity.com/paper/2607.20538/) (2026)
- [DynaCalKV: Key-Value Cache Compression via Head Grouping and Adaptive Rank Allocation](https://mlsanity.com/paper/2607.24331/) (2026)
- [VestigeKV: The NoPE-MLA KV Cache Carries Its Own Sparse-Attention Signal in a Vestigial Branch](https://mlsanity.com/paper/2609.03949/) (2026)
- [MILO: Efficient Many-shot In-Context Learning with Block-wise Low-rank Compression](https://mlsanity.com/paper/2609.29913/) (2026)
- [DimPO: Dimensionality Reduction for Attention using Preference Optimization](https://mlsanity.com/paper/2609.32579/) (2026)
- [Telescopic Language Models](https://mlsanity.com/paper/2609.35769/) (2026)
- [AttSVD:Prompt-Adaptive Low-Rank KV Cache Compression via Attention-Guided SVD](https://mlsanity.com/paper/2610.06927/) (2026)

## Abstract (arXiv)

KV cache has become a de facto technique for the inference of large language models (LLMs), where tensors of shape (layer number, head number, sequence length, feature dimension) are introduced to cache historical information for self-attention. As the size of the model and data grows, the KV cache can quickly become a bottleneck within the system in both storage and memory transfer. To address this, prior studies usually focus on the first three axes of the cache tensors for compression. This paper supplements them, focusing on the feature dimension axis, by utilizing low-rank projection matrices to transform the cache features into spaces with reduced dimensions. We begin by investigating the canonical orthogonal projection method for data compression through principal component analysis (PCA). We observe the issue with PCA projection where significant performance degradation is observed at low compression rates. To bridge the gap, we propose to directly tune the orthogonal projection matrices with a distillation objective using an elaborate Matryoshka training strategy. After training, we adaptively search for the optimal compression rates for various layers and heads given varying compression budgets. Compared to previous works, our method can easily embrace pre-trained LLMs and hold a smooth tradeoff between performance and compression rate. We empirically witness the high data efficiency of our training procedure and find that our method can sustain over 90% performance with an average KV cache compression rate of 60% (and up to 75% in certain extreme scenarios) for popular LLMs like LLaMA2-7B-base and Mistral-7B-v0.3-base.