# LazyEviction: Lagged KV Eviction with Attention Pattern Observation for Efficient Long Reasoning

arXiv: https://arxiv.org/abs/2506.15969 · HTML: https://mlsanity.com/paper/2506.15969/

## Key facts

- Cited by 16 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 37 of its 44 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## 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 / [Efficient reasoning and agent inference](https://mlsanity.com/inference/efficient-reasoning-and-agent-inference/)

## Builds on (most cited first, 30 of 37)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (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)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [Quest: Query-Aware Sparsity for Efficient Long-Context LLM Inference](https://mlsanity.com/paper/2406.10774/) (2024)
- [Scissorhands: Exploiting the Persistence of Importance Hypothesis for LLM KV Cache Compression at Test Time](https://mlsanity.com/paper/2305.17118/) (2023)
- [PyramidKV: Dynamic KV Cache Compression based on Pyramidal Information Funneling](https://mlsanity.com/paper/2406.02069/) (2024)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [TokenSkip: Controllable Chain-of-Thought Compression in LLMs](https://mlsanity.com/paper/2502.12067/) (2025)
- [Token-Budget-Aware LLM Reasoning](https://mlsanity.com/paper/2412.18547/) (2024)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [Compressed Chain of Thought: Efficient Reasoning Through Dense Representations](https://mlsanity.com/paper/2412.13171/) (2024)
- [Keyformer: KV Cache Reduction through Key Tokens Selection for Efficient Generative Inference](https://mlsanity.com/paper/2403.09054/) (2024)
- [Transformers are Multi-State RNNs](https://mlsanity.com/paper/2401.06104/) (2024)
- [Sketch-of-Thought: Efficient LLM Reasoning with Adaptive Cognitive-Inspired Sketching](https://mlsanity.com/paper/2503.05179/) (2025)
- [SoftCoT: Soft Chain-of-Thought for Efficient Reasoning with LLMs](https://mlsanity.com/paper/2502.12134/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)

## Built on by (most cited first, 16 of 16)

- [ThinKV: Thought-Adaptive KV Cache Compression for Efficient Reasoning Models](https://mlsanity.com/paper/2510.01290/) (2025)
- [TriAttention: Efficient Long Reasoning with Trigonometric KV Compression](https://mlsanity.com/paper/2604.04921/) (2026)
- [MEMENTO: Teaching LLMs to Manage Their Own Context](https://mlsanity.com/paper/2604.09852/) (2026)
- [SideQuest: Model-Driven KV Cache Management for Long-Horizon Agentic Reasoning](https://mlsanity.com/paper/2602.22603/) (2026)
- [Think How to Think: Mitigating Overthinking with Autonomous Difficulty Cognition in Large Reasoning Models](https://mlsanity.com/paper/2507.02663/) (2025)
- [ReasonAlloc: Hierarchical Decoding-Time KV Cache Budget Allocation for Reasoning Models](https://mlsanity.com/paper/2606.11164/) (2026)
- [HARD-KV: Head-Adaptive Regularization for Decoding-time KV Compression](https://mlsanity.com/paper/2606.28831/) (2026)
- [LOCKS: Page-Local Compact Key Summaries for Efficient Long-Context Decoding](https://mlsanity.com/paper/2607.24555/) (2026)
- [Random Attention: Rethinking KV Cache Eviction for Efficient Reasoning](https://mlsanity.com/paper/2609.03430/) (2026)
- [State commitment learning: training language models to distinguish computation from memory](https://mlsanity.com/paper/2606.05201/) (2026)
- [GrowPage: On-Demand KV Budgeting for Efficient LLM Reasoning Serving](https://mlsanity.com/paper/2609.03494/) (2026)
- [BeaconKV: Key-Value Cache Compression Guided by Beacon Queries for Efficient Large Reasoning Model Inference](https://mlsanity.com/paper/2609.04971/) (2026)
- [StepKV: Step-Aware KV Cache Compression for LLM Agents](https://mlsanity.com/paper/2609.22158/) (2026)
- [CORE: COverage CAlibration and Evicted-Mass REdistribution for KV Cache](https://mlsanity.com/paper/2610.02235/) (2026)
- [AvoKV-E: Payload-Aware KV Cache Eviction for Long Reasoning](https://mlsanity.com/paper/2610.03007/) (2026)
- [Spend Bytes on Breadth: Precision-Count Trade-offs for Decode-Time KV Compression in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2610.05685/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) exhibit enhanced capabilities by Chain-of-Thought reasoning. However, the extended reasoning sequences introduce significant GPU memory overhead due to increased key-value (KV) cache. Existing KV cache compression methods mitigate memory bottlenecks but struggle in long reasoning tasks. In this paper, we analyze attention patterns in reasoning tasks and reveal a Token Importance Recurrence phenomenon: a large proportion of tokens regain high attention after multiple decoding steps, which is failed to capture by existing works and may lead to unpredictable eviction on such periodically critical tokens. To address this, we propose LazyEviction, an observation window-based lagged eviction framework retaining latent recurring tokens by prioritized eviction based on tokens' recurrence patterns. Extensive experiments demonstrate that LazyEviction reduces KV cache by 50%~70% while maintaining comparable accuracy, outperforming existing KV cache compression baselines. Our implementation code can be found at https://github.com/Halo-949/LazyEviction.