# MomentKV: Closing the Directional Gap in KV Cache Eviction for Long-Context Inference

arXiv: https://arxiv.org/abs/2606.01563 · HTML: https://mlsanity.com/paper/2606.01563/

## Key facts

- Cited by 6 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 29 of its 33 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [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)
- [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)
- [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)
- [Ada-KV: Optimizing KV Cache Eviction by Adaptive Budget Allocation for Efficient LLM Inference](https://mlsanity.com/paper/2407.11550/) (2024)
- [Cost-Efficient Large Language Model Serving for Multi-turn Conversations with CachedAttention](https://mlsanity.com/paper/2403.19708/) (2024)
- [A Survey on Large Language Model Acceleration based on KV Cache Management](https://mlsanity.com/paper/2412.19442/) (2024)
- [Dynamic Memory Compression: Retrofitting LLMs for Accelerated Inference](https://mlsanity.com/paper/2403.09636/) (2024)
- [Model Tells You Where to Merge: Adaptive KV Cache Merging for LLMs on Long-Context Tasks](https://mlsanity.com/paper/2407.08454/) (2024)
- [A Simple and Effective L2 Norm-Based Strategy for KV Cache Compression](https://mlsanity.com/paper/2406.11430/) (2024)
- [Palu: Compressing KV-Cache with Low-Rank Projection](https://mlsanity.com/paper/2407.21118/) (2024)
- [KeyDiff: Key Similarity-Based KV Cache Eviction for Long-Context LLM Inference in Resource-Constrained Environments](https://mlsanity.com/paper/2504.15364/) (2025)
- [KV Cache Compression, But What Must We Give in Return? A Comprehensive Benchmark of Long Context Capable Approaches](https://mlsanity.com/paper/2407.01527/) (2024)
- [Compute Or Load KV Cache? Why Not Both?](https://mlsanity.com/paper/2410.03065/) (2024)
- [Taming the Fragility of KV Cache Eviction in LLM Inference](https://mlsanity.com/paper/2510.13334/) (2025)
- [CAOTE: KV Cache Selection for LLMs via Attention Output Error-Based Token Eviction](https://mlsanity.com/paper/2504.14051/) (2025)
- [When Right Meets Wrong: Bilateral Context Conditioning with Reward-Confidence Correction for GRPO](https://mlsanity.com/paper/2603.13134/) (2026)
- [When Does Value-Aware KV Eviction Help? A Fixed-Contract Diagnostic for Non-Monotone Cache Compression](https://mlsanity.com/paper/2605.08234/) (2026)
- [Breaking the Memory Wall: A Study of I/O Patterns and GPU Memory Utilization for Hybrid CPU-GPU Offloaded Optimizers](https://mlsanity.com/paper/2406.10728/) (2024)
- [Towards understanding how attention mechanism works in deep learning](https://mlsanity.com/paper/2412.18288/) (2024)

## Built on by (most cited first, 6 of 6)

- [Error Certificates for KV-Cache Eviction via Randomized Design](https://mlsanity.com/paper/2607.21475/) (2026)
- [PatchKV: Weight-Space Compensation of KV Cache](https://mlsanity.com/paper/2609.39329/) (2026)
- [Learning What Matters: Supervising Global Context Pruning with Causal Evidence Sets](https://mlsanity.com/paper/2607.21692/) (2026)
- [PAGE: Partition-Aware Gated KV-Cache Eviction](https://mlsanity.com/paper/2609.22157/) (2026)
- [CORE: COverage CAlibration and Evicted-Mass REdistribution for KV Cache](https://mlsanity.com/paper/2610.02235/) (2026)
- [KVFetch: Temporal Prefetching for the Missing Half of KV Cache Compression](https://mlsanity.com/paper/2610.08811/) (2026)

## Abstract (arXiv)

Autoregressive decoding in Transformer-based language models relies on the KV cache, whose memory footprint grows linearly with sequence length and becomes the primary bottleneck for long-context inference. KV cache eviction addresses this by retaining a fixed-size subset of key-value pairs and discarding the rest. We identify that a primary source of output degradation is not the residual attention mass on evicted tokens, which existing methods already minimize, but a directional mismatch between the retained and evicted token sets. Specifically, the evicted tokens in practice are often near-orthogonal to the retained ones. Thus, even a small evicted mass could have an oversized impact on the resulting direction distribution and amplify into substantial output error. This reveals a fundamental limit in existing strategies. To address this, we propose MomentKV, which maintains compact, small-size moment statistics over the evicted token set, including a count, key mean, value mean, and value-key covariance. During eviction, the moment statistics is leveraged to identify tokens already well aligned with and captured by the accumulated summary, keeping the evicted set geometrically regular. During inference, they yield a closed-form first-order approximation of the evicted attention output, forming a mutually reinforcing loop between selective eviction and accurate correction. On LongBench and RULER with LLaMA-3.1-8B-Instruct and Qwen3-4B-Instruct, MomentKV outperforms all baselines at every cache budget, with the largest gains under aggressive compression.