# OjaKV: Context-Aware Online Low-Rank KV Cache Compression

arXiv: https://arxiv.org/abs/2509.21623 · HTML: https://mlsanity.com/paper/2509.21623/

## Key facts

- Cited by 7 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 21 of its 37 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [SnapKV: LLM Knows What You are Looking for Before Generation](https://mlsanity.com/paper/2404.14469/) (2024)
- [H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models](https://mlsanity.com/paper/2306.14048/) (2023)
- [KIVI: A Tuning-Free Asymmetric 2bit Quantization for KV Cache](https://mlsanity.com/paper/2402.02750/) (2024)
- [KVQuant: Towards 10 Million Context Length LLM Inference with KV Cache Quantization](https://mlsanity.com/paper/2401.18079/) (2024)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Using an LLM to Help With Code Understanding](https://mlsanity.com/paper/2307.08177/) (2023)
- [Lessons from the Trenches on Reproducible Evaluation of Language Models](https://mlsanity.com/paper/2405.14782/) (2024)
- [ShadowKV: KV Cache in Shadows for High-Throughput Long-Context LLM Inference](https://mlsanity.com/paper/2410.21465/) (2024)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [Keep the Cost Down: A Review on Methods to Optimize LLM' s KV-Cache Consumption](https://mlsanity.com/paper/2407.18003/) (2024)
- [Eigen Attention: Attention in Low-Rank Space for KV Cache Compression](https://mlsanity.com/paper/2408.05646/) (2024)
- [MatryoshkaKV: Adaptive KV Compression via Trainable Orthogonal Projection](https://mlsanity.com/paper/2410.14731/) (2024)
- [MedSyn: LLM-based Synthetic Medical Text Generation Framework](https://mlsanity.com/paper/2408.02056/) (2024)
- [ReCalKV: Low-Rank KV Cache Compression via Head Reordering and Offline Calibration](https://mlsanity.com/paper/2505.24357/) (2025)
- [Copilot Evaluation Harness: Evaluating LLM-Guided Software Programming](https://mlsanity.com/paper/2402.14261/) (2024)

## Built on by (most cited first, 7 of 7)

- [Attention Sink in Transformers: A Survey on Utilization, Interpretation, and Mitigation](https://mlsanity.com/paper/2604.10098/) (2026)
- [eOptShrinkQ: Near-Lossless KV Cache Compression Through Optimal Spectral Denoising and Quantization](https://mlsanity.com/paper/2605.02905/) (2026)
- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [ZoomR: Memory Efficient Reasoning through Multi-Granularity Key Value Retrieval](https://mlsanity.com/paper/2604.10898/) (2026)
- [VarRate: Training-Free Variable-Rate KV Cache Compression for Long-Context LLMs](https://mlsanity.com/paper/2607.15498/) (2026)
- [PuzzleKV: Page-Wise Low-Rank Decomposition for KV Cache Compression](https://mlsanity.com/paper/2608.23843/) (2026)
- [TierKV: Long-Context On-Device LLMs via Predictive Multi-Tier KV Caching](https://mlsanity.com/paper/2609.21172/) (2026)

## Abstract (arXiv)

The expanding long-context capabilities of large language models are constrained by a significant memory bottleneck: the key-value (KV) cache required for autoregressive generation. This bottleneck is substantial; for instance, a Llama-3.1-8B model processing a 32K-token prompt at a batch size of 4 requires approximately 16GB for its KV cache, a size exceeding the model's weights. While KV-cache compression via low-rank projection is a promising direction, existing methods rely on a static, offline-learned subspace that performs poorly under data distribution shifts. To overcome these limitations, we introduce OjaKV, a novel framework that integrates a strategic hybrid storage policy with online subspace adaptation. First, OjaKV recognizes that not all tokens are equally important for compression; it preserves the crucial first and most recent tokens in full-rank, maintaining high-fidelity anchors for attention. Second, for the vast majority of intermediate tokens, it applies low-rank compression by incrementally adapting the projection basis using Oja's algorithm for online principal component analysis. This adaptation involves a comprehensive update during prompt prefilling and lightweight periodic updates during decoding, ensuring the subspace remains aligned with the evolving context. Crucially, our framework is fully compatible with modern attention modules like FlashAttention. Experiments demonstrate that OjaKV maintains or even improves zero-shot accuracy at high compression ratios. In particular, OjaKV achieves its strongest gains on very long-context benchmarks that require complex reasoning, highlighting the importance of online subspace adaptation in dynamically tracking context shifts. These results establish our hybrid framework as a practical, plug-and-play solution for memory-efficient long-context inference without requiring model fine-tuning.